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

Figures from this paper

References

SHOWING 1-10 OF 19 REFERENCES
A counter-example to ‘Wagner's conjecture’ for infinite graphs
  • 28
Classes of locally finite ubiquitous graphs
  • Thomas Andreae
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 2013
  • 6
  • PDF
Graph-theoretical versus topological ends of graphs
  • 90
  • PDF
A problem concerning infinite graphs
  • J. Lake
  • Computer Science, Mathematics
  • Discret. Math.
  • 1976
  • 16
Über eine eigenschaft lokalfiniter, unendlicher bäume
  • Th. Andreae
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1979
  • 9
  • Highly Influential
A compactness theorem for singular cardinals, free algebras, Whitehead problem and tranversals
  • 160
On well-quasi-ordering finite trees
  • 326
  • Highly Influential
On disjoint configurations in infinite graphs
  • 6
  • Highly Influential
...
1
2
...