3 citations · 5 across the 3 of their papers we have counts for
6 papers
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.…
Hamilton decompositions of one-ended Cayley graphs
Joshua Erde, Florian Lehner, Max Pitz
We prove that any one-ended, locally finite Cayley graph with non-torsion generators admits a decomposition into edge-disjoint Hamiltonian (i.e. spanning) double-rays. In particula…
Firefighting on trees and Cayley graphs
Florian Lehner
We study Hartnell's firefighter problem on infinite trees and characterise the branching number in terms of the firefighting game. Using our results about trees, we give a partial…
A counterexample to Montgomery's conjecture on dynamic colourings of regular graphs
Nathan Bowler, Joshua Erde, Florian Lehner +3
A \emph{dynamic colouring} of a graph is a proper colouring in which no neighbourhood of a non-leaf vertex is monochromatic. The \emph{dynamic colouring number} of a graph…
Breaking graph symmetries by edge colourings
Florian Lehner
The distinguishing index of a graph is the least number of colours needed in an edge colouring which is not preserved by any non-trivial automorphism. Broere and Pilśni…
Distinguishing graphs with intermediate growth
Florian Lehner
A graph G is said to be 2-distinguishable if there is a 2-labeling of its vertices which is not preserved by any nontrivial automorphism of G. We show that every locally finite gra…