Reconfiguring Independent Sets in Claw-Free Graphs.

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in S) such that the result is again an independent set. We also consider the more restricted model where v and w have to be adjacent.