Forcing a Kr minor by high external connectivity

We investigate the minimal structure a graph H is required to have if H is to force a large complete minor in any graph in which it has high external connectivity. We observe that such graphs H must contain a large binary tree with some small additions, and prove that some canonical instances of this structure are also sufficient to force a large complete minor. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 241–264, 2002; DOI 10.1002/jgt.10026