introduction of some one-searchable graphs

Search graph problems are usually modeled in the form of on-graph games between oneescaping thief and some police officers. police intends to arrest the thief while the real goal of robber isprevention from arrest. as it has been evaluated in this paper, it is known as cops robber game. thereare two specific characteristics for this play which may separate it from others. firstly it has unlimitedspeed and secondly all players have special playing time.