3 citations · 5 across the 7 of their papers we have counts for
19 papers · 1 filter
A note on classes of subgraphs of locally finite graphs
Florian Lehner
We investigate the question how `small' a graph can be, if it contains all members of a given class of locally finite graphs as subgraphs or induced subgraphs. More precisely, we g…
Universal planar graphs for the topological minor relation
Florian Lehner
Huynh et al. recently showed that a countable graph which contains every countable planar graph as a subgraph must contain arbitrarily large finite complete graphs as topologic…
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups
Joshua Erde, Florian Lehner
A well-known conjecture of Alspach says that every -regular Cayley graph of an abelian group can be decomposed into Hamiltonian cycles. We consider an analogous question for in…
On fixity of arc-transitive graphs
Florian Lehner, Primoz Potocnik, Pablo Spiga
The relative fixity of a permutation group is the maximum proportion of the points fixed by a non-trivial element of the group and the relative fixity of a graph is the relative fi…
On asymmetric colourings of graphs with bounded degrees and infinite motion
Florian Lehner, Monika Pilśniak, Marcin Stawiski
A vertex colouring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Tucker conjectured that if every automorphism of a connected, locall…
Bounding the cop number of a graph by its genus
Nathan Bowler, Joshua Erde, Florian Lehner +1
It is known that the cop number of a connected graph can be bounded as a function of the genus of the graph . The best known bound, that $c(G) \leq \left\lfloor \f…