Neighborhood unions and disjoint chorded cycles in graphs

Let s ≥ 0 , t ≥ 0 be two integers and G be a graph with at least 3 s + 4 t vertices. In this paper, we show that if | N ( u , G ) ∪ N ( v , G ) | ≥ 3 s + 4 t + 1 for any two nonadjacent vertices u and v in G , then G contains s + t vertex-disjoint cycles such that t of them are chorded cycles. The condition is sharp.