Neighborhood unions and disjoint chorded cycles in graphs

Let s≥0,t≥0s≥0,t≥0 be two integers and GG be a graph with at least 3s+4t3s+4t vertices. In this paper, we show that if |N(u,G)∪N(v,G)|≥3s+4t+1|N(u,G)∪N(v,G)|≥3s+4t+1 for any two nonadjacent vertices uu and vv in GG, then GG contains s+ts+t vertex-disjoint cycles such that tt of them are chorded cycles. The condition is sharp.