2018/09/03 by Bowler, Nathan, Elbracht, Christian, Erde, Joshua +4
#05C63 #05C83 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.00602
A graph G is said to be \preceq-ubiquitous, where \preceq is the minor relation between graphs, if whenever Γ is a graph with nG \preceq Γ for all n ∈ ℕ, then one also has ℵ0 G \preceq Γ, where αG is the disjoint union of α many copies of G. A well-known conjecture of Andreae is that every locally finite connected graph is \preceq-ubiquitous. In this paper we give a sufficient condition on the structure of the ends of a graph~G which implies that G is \preceq-ubiquitous. In particular this implies that the full grid is \preceq-ubiquitous.