For line arrangements without (k-1)-fold or k-fold points, the Levi graph has an induced 8-cycle; further bounds and exact longest-cycle lengths are given for generic, Hesse, Ceva, and supersolvable arrangements.
On some of my favourite problems in various branches of combinatorics
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On induced cycles of Levi graphs associated to line arrangements
For line arrangements without (k-1)-fold or k-fold points, the Levi graph has an induced 8-cycle; further bounds and exact longest-cycle lengths are given for generic, Hesse, Ceva, and supersolvable arrangements.