Happy Ending or Many Concurrent Lines

Abstract

For each $n\ge 2$, $l\ge 3$, let ${ES}_L(l,n)$ be the minimum $N$ such that every family of $N$-lines in the plane contains either $l$ concurrent lines or $n$ lines in convex position. In this papar, we give the upper and lower bounds for $E{S}_L(l,n)$. This is one of the extensions of the line version of Erdös-Szekeres convex polygon problem.