The maximum number of copies of an even cycle in a planar graph

TL;DR

This paper determines the maximum number of even cycle copies in large planar graphs, resolving a conjecture and providing asymptotic results for all cycle lengths.

Contribution

It asymptotically solves a conjecture by Cox and Martin on the maximum copies of even cycles in planar graphs.

Findings

Asymptotic maximum number of even cycle copies in planar graphs established

Conjecture of Cox and Martin resolved for all cycle lengths

Provides new bounds and structural insights into planar graph cycles

Abstract

We resolve a conjecture of Cox and Martin by determining asymptotically for every $k\ge 2$ the maximum number of copies of $C_{2k}$ in an $n$-vertex planar graph.