Unavoidable minors for connected 2-polymatroids

Abstract It is well known that, for any integer n greater than one, there is a number r such that every 2-connected simple graph with at least r edges has a minor isomorphic to an n-edge cycle or K 2 , n . This result was extended to matroids by Lovasz, Schrijver, and Seymour who proved that every sufficiently large connected matroid has an n-element circuit or an n-element cocircuit as a minor. In this paper, we generalize these theorems by providing an analogous result for connected 2-polymatroids. Significant progress on the corresponding problem for k-polymatroids is also described.