Constructions of point-line arrangements in the plane with large girth

Mozhgan Mirzaei, Andrew Suk, Jacques Verstraëte

A classical result by Erdős, and later on by Bondy and Simonivits, states that every $n$-vertex graph with no cycle of length $2k$ has at most $O(n^{1+1/k})$ edges. This bound is…