Disjoint unions of complete minors Original Research Article

Given integers r and s, and n large compared to r and s, we determine the maximum size of a graph of order n having no minor isomorphic to image, the union of s disjoint copies of image. The extremal function depends on the relative sizes of r and s. If s is small compared to r the extremal function is essentially independent of s. On the other hand, if s is large compared to r, there is a unique extremal graph image; this assertion is a generalization of the case image which is a classical result of Erdős and Pósa.