Independence number and vertex-disjoint cycles

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