### Abstract

Suppose that we are given two independent sets I_{b} and I_{r} of a graph such that |Ib|=|Ir|, and imagine that a token is placed on each vertex in I_{b}. Then, the sliding token problem is to determine whether there exists a sequence of independent sets which transforms I_{b} into I_{r} 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 paper, we thus study the problem restricted to trees, and give the following three results: (1) the decision problem is solvable in linear time; (2) for a yes-instance, we can find in quadratic time an actual sequence of independent sets between I_{b} and I_{r} whose length (i.e., the number of token-slides) is quadratic; and (3) there exists an infinite family of instances on paths for which any sequence requires quadratic length.

Original language | English |
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Pages (from-to) | 132-142 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 600 |

DOIs | |

Publication status | Published - Oct 4 2015 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*600*, 132-142. https://doi.org/10.1016/j.tcs.2015.07.037