Multi-Color Pebble Motion on Graphs

We consider a graph with n vertices, and p<n pebbles of m colors. A pebble move consists of transferring a pebble from its current host vertex to an adjacent unoccupied vertex. The problem is to move the pebbles to a given new color arrangement.We study the feasibility version of the problem—does a given instance have a solution? We use an algorithm of Auletta et al. (Algorithmica 23:223–245, 1999) for the problem where each pebble has a distinct color to give a linear time algorithm for the feasibility decision problem on a general graph.

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