Predavatelj: Florian Lehner (TU Graz, Avstrija)
A basic question related to this game is to characterize the class of graphs for which the cop has a winning strategy. For finite graphs it has been shown by Nowakowski and Winkler these are exactly the constructible graphs.
For infinite graphs, Chastand et al introduced a modification of the winning criterion for which they conjectured the same to be true. We disprove this conjecture and suggest a further modification in the same spirit for which we show that the cop has a winning strategy on every constructible graph.