3 citations · 5 across the 9 of their papers we have counts for
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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…
A bound for the distinguishing index of regular graphs
Florian Lehner, Monika Pilśniak, Marcin Stawiski
An edge-colouring of a graph is distinguishing, if the only automorphism which preserves the colouring is the identity. It has been conjectured that all but finitely many connected…
On the cop number of toroidal graphs
Florian Lehner
We show that the cop number of toroidal graphs is at most 3. This resolves a conjecture by Schroeder from 2001 which is implicit in a question by Andreae from 1986.