A long cycle theorem involving Fan-type degree condition and neighborhood intersection

TL;DR

This paper introduces a new sufficient condition combining Fan-type degree criteria and neighborhood intersection to guarantee the existence of long cycles in graphs.

Contribution

It presents a novel theorem that extends existing conditions for long cycles by integrating Fan-type degree and neighborhood intersection criteria.

Findings

New sufficient condition for long cycles in graphs

Extension of Fan-type degree conditions

Applicable to broader classes of graphs

Abstract

In this short note, we give a new sufficient condition for the existence of long cycles in graphs involving Fan-type degree condition and neighborhood intersection.