Ubiquity of graphs with nowhere‐linear end structure

Abstract

AbstractA graph is said to be ‐ubiquitous, where is the minor relation between graphs, if whenever is a graph with for all , then one also has , where is the disjoint union of many copies of . A well‐known conjecture of Andreae is that every locally finite connected graph is ‐ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph which implies that is ‐ubiquitous. In particular this implies that the full‐grid is ‐ubiquitous.