Abstract: In 1963, Corrądi and Hajnal showed that for every positive integer $k$, each graph on at least $3k$ vertices with minimum degree at least $2k$ must contain $k$ vertex-disjoint cycles. This result is sharp in terms of both the number of vertices and the minimum degree. Recently, Kierstead, Kostochka, and Yeager characterized the sharpness examples of this statement, in which the main family of sharpness examples contains a 'large' independent set. Thus, it natural to believe that one can further lower the minimum degree of Corrądi-Hajnal and still obtain $k$ vertex-disjoint cycles, provided the indepence number of graph is not too big. Recent work by Balogh et al. has shown this to be true when the graph is 'dense' (i.e., $k \approx n/3$). In this talk, we will explore a sparse version of this result, and present several other possible extensions to chorded cycles as well as a 'mixed' version.