Cops, robber and traps

Abstract

In this version of the Cops and Robber game, traps can be placed on any vertex by a Cop. If the Robber ever occupies the same vertex then he is caught. We show that one Cop and a fixed number of traps are not enough to capture a Robber on a graph that requires two Cops without traps. We give several results concerning the relationship between the number of Cops and traps and the retracts of a graph. We also give a sufficient condition for one Cop and one trap to be able to capture a Robber. We conjecture that this is a necessary condition as well.