On Complete S-Reachable Graphs

Abstract

We consider a variant of pebble motion game on a simple connected undirected graph. A configuration in such a graph indicates the placement of a robot and a hole at two different vertices and obstacles at the remaining vertices. A graph is said to be complete S-reachable if starting from any configuration the robot can be taken to any other vertex by a sequence of moves consisting of simple moves of the obstacles and mRJ moves of the robot for m ∈ S, where S is a finite non-empty set of non-negative integers. An mRJ move is the process of moving the robot from a vertex to another vertex along a path by jumping over m obstacles. The 0RJ move is known as a simple move. We identify some classes of graphs that are complete {m}-reachable.