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Ubiquity of graphs with nowhere-linear end structure
Nathan Bowler1, Christian Elbracht1, Joshua Erde2
1Department of Mathematics Universität Hamburg Hamburg Germany.
Abstract:
A 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.
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