Independence number and vertex-disjoint cycles Original Research Article

In this paper we consider graphs which have no k vertex-disjoint cycles. For given integers image let image be the maximum order of a graph G with independence number image, which has no k vertex-disjoint cycles. We prove that image if image or image, and image in general. We also prove the following results: (1) there exists a constant image (depending only on image) such that image, (2) there exists a constant image (depending only on k) such that image, and (3) there exists no absolute constant c such that image.