GD 2012: Graph Drawing pp 352-363

# Density Theorems for Intersection Graphs of t-Monotone Curves

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

## 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 n t-monotone curves with at least εn 2 intersecting pairs (disjoint pairs), then there exists two subfamilies F 1,F 2 ⊂ F of size δn each, such that every curve in F 1 intersects (is disjoint to) every curve in F 2, where δ depends only on ε. We apply these results to find pairwise disjoint edges in simple topological graphs.

## Keywords

Intersection Graph Density Theorem Topological Graph Left Endpoint Disjoint Edge
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

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