Normal tree orders for infinite graphs

Abstract

A well-founded tree T denned on the vertex set of a graph G is called normal if the endvertices of any edge of G are comparable in T. We study how normal trees can be used to describe the structure of infinite graphs.In particular, we extend Jung's classical existence theorem for trees of height w to trees of arbitrary height.Applications include a structure theorem for graphs without large complete topological minors.A number of open problems are suggested.