A Note on Neighborhood Unions and Independent Cycles

Abstract

We prove that if \(G\) is a simple graph of order \(n \geq 3k\) such that \(|N(x) \cup N(y)| \geq 3k\) for all nonadjacent pairs of vertices \(x\) and \(y\), then \(G\) contains \(k\) vertex-independent cycles.