Cops and an Insightful Robber

The ‘Cheating Robot’ version of Cops and Robbers is played on a finite, simple, connected graph. players move in the same time period. However, before moving, robot observes to which vertices cops are moving it fast enough complete its also know that will use this information. More required capture than robber. Indeed, minimum degree lower bound number robot. Only tree one cop guaranteed robot, although two sufficient both robber outerplanar graphs. In graphs where retracts involved, we show how strategies against can be modified This approach gives exact numbers for hypercubes, k-dimensional grids general.