12 citations · 23 across the 23 of their papers we have counts for
39 papers
Countable Graphs with Finite Path-width: Characterisation and Universality
Tony Huynh, Freddie Illingworth, Nikolai Karol +4
We study path-width and the closely related parameter line-width in countably infinite graphs. Our first result characterises the graphs of finite path-width: they are the graphs t…
The 2-Cops-Move Cop Number of Graphs on the Torus, Klein Bottle, and Projective Plane
Florian Lehner, Alan Sun
We study the -cops-move variant of the game of cops and robber, in which at most two cops may move in each turn. Let denote the corresponding cop number. We prove that…
Chromatic number is not tournament-local
António Girão, Kevin Hendrey, Freddie Illingworth +4
Scott and Seymour conjectured the existence of a function such that, for every graph and tournament on the same vertex set, $χ(G) \geqs…
Asymmetrizing infinite trees
Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2
A graph is asymmetrizable if it has a set of vertices whose setwise stablizer only consists of the identity automorphism. The motion of a graph is the minimum number of ver…
Asymmetric colouring of locally compact permutation groups
Florian Lehner
Let for a countable set . Call a colouring of asymmetric, if the identity is the only element of which preserves all colours. The motion (also…
Tipsy cop and tipsy robber: collisions of biased random walks on graphs
Pamela E. Harris, Erik Insko, Florian Lehner
Introduced by Harris, Insko, Prieto Langarica, Stoisavljevic, and Sullivan, the \emph{tipsy cop and drunken robber} is a variant of the cop and robber game on graphs in which the r…