Cycles in graphs of fixed girth with large size

TL;DR

This paper establishes an optimal asymptotic lower bound on the number of even cycles of any fixed length in large graphs with a fixed girth, advancing understanding of cycle distribution in such graphs.

Contribution

It provides the first optimal lower bound on the count of even cycles of fixed length in graphs with fixed girth as the number of vertices grows.

Findings

Derived an asymptotically optimal lower bound for even cycles

Applied to graphs with fixed girth and large size

Enhances understanding of cycle distribution in extremal graph theory

Abstract

Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.