On induced cycles of Levi graphs associated to line arrangements

TL;DR

This paper studies the presence and length of induced cycles in Levi graphs derived from line arrangements in complex projective planes, contributing to the understanding of their combinatorial structure.

Contribution

It introduces new results on the existence and maximal length of induced cycles in Levi graphs related to line arrangements.

Findings

Identifies conditions for the existence of induced cycles.

Determines the maximum length of induced cycles in these graphs.

Provides new bounds and characterizations for Levi graphs.

Abstract

In this article, we investigate the existence of induced cycles in Levi graphs associated to line arrangements in $\mathbb{P}_{\mathbb{C}}^2$. We also look at the problem of finding the length of a longest induced cycle in Levi graphs associated to line arrangements.