Author:
Ackerman Eyal,Keszegh Balázs
Abstract
Let $\cC$ be a set of curves in the plane such that no three curves in $\cC$ intersect at a single point and every pair of curves in $\cC$ intersect at exactly one point which is either a crossing or a touching point. According to a conjecture of J\'anos Pach the number of pairs of curves in $\cC$ that touch each other is $O(|\cC|)$. We prove this conjecture for $x$-monotone curves.
Cited by
1 articles.
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1. On the number of tangencies among 1-intersecting curves;Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications;2023