3 citations · 5 across the 9 of their papers we have counts for
6 papers · 1 filter
A Stallings' type theorem for quasi-transitive graphs
Matthias Hamann, Florian Lehner, Babak Miraftab +1
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This ca…
Invariant spanning double rays in amenable groups
Agelos Georgakopoulos, Florian Lehner
A well-known result of Benjamini, Lyons, Peres, and Schramm states that if is a finitely generated Cayley graph of a group , then is amenable if and only if admits a…
Distinguishing infinite graphs with bounded degrees
Florian Lehner, Monika Pilśniak, Marcin Stawiski
Call a colouring of a graph distinguishing, if the only colour preserving automorphism is the identity. A conjecture of Tucker states that if every automorphism of a graph move…
Distinguishing numbers of finite -valent vertex-transitive graphs
Florian Lehner, Gabriel Verret
The distinguishing number of a graph is the smallest such that admits a -colouring for which the only colour-preserving automorphism of is the identity. We deter…
On symmetries of edge and vertex colourings of graphs
Florian Lehner, Simon M. Smith
Let and be edge or vertex colourings of a graph . We say that is less symmetric than if the stabiliser (in ) of is contained in the…
Distinguishing density and the Distinct Spheres Condition
Wilfried Imrich, Florian Lehner, Simon M. Smith
If a graph has distinguishing number 2, then there exists a partition of its vertex set into two parts, such that no nontrivial automorphism of fixes setwise the two parts.…