Corpus ID: 119652837

# Ubiquity in graphs I: Topological ubiquity of trees

@article{Bowler2018UbiquityIG,
title={Ubiquity in graphs I: Topological ubiquity of trees},
author={N. Bowler and Christian Elbracht and Joshua Erde and Pascal Gollin and K. Heuer and Max Pitz and Maximilian Teegen},
journal={arXiv: Combinatorics},
year={2018}
}
Let $\triangleleft$ be a relation between graphs. We say a graph $G$ is \emph{$\triangleleft$-ubiquitous} if whenever $\Gamma$ is a graph with $nG \triangleleft \Gamma$ for all $n \in \mathbb{N}$, then one also has $\aleph_0 G \triangleleft \Gamma$, where $\alpha G$ is the disjoint union of $\alpha$ many copies of $G$. The \emph{Ubiquity Conjecture} of Andreae, a well-known open problem in the theory of infinite graphs, asserts that every locally finite connected graph is ubiquitous with… Expand
5 Citations

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