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.
Citation
Jill R.Faudree, Ronald J.Gould. A Note on Neighborhood Unions and Independent Cycles[J], Ars Combinatoria, Volume 076. 29-31. .
