Gena Hahn, Cops, robbers, infinite graphs and related problems

We briefly survey the game of cops-and-robbers on graphs and its variants in the fi nite case and then concenrate on in finite graphs, stressing the diff erence between the fi nite and the in finite. Along the way we show (time allowing) how to construct in finite vertex transitive graphs from any graphs and point out some strange properties of the construction. We also suggest several open problems, both fi nite and infi nite. The talk is based on work with A. Bonato, C.Tardif and R.E. Woodrow.