Suppose that we are given two independent sets Ib and Ir of a graph such that |Ib|=|Ir|, and imagine that a token is placed on each vertex in Ib. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms Ib into Ir so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph. This problem is known to be PSPACE-complete even for planar graphs, and also for bounded treewidth graphs. In this talk, we thus study the problem restricted to trees, and give the following three results:
(Based on a paper from ISAAC 2014 and Theoretical Computer Science 2015 by Demaine, Demaine, Fox-Epstein, Hoang, Ito, Ono, Otachi, Uehara, and Yamada.)