### Abstract

Suppose that we are given two independent sets I^{0} and I^{r} of a graph such that |I^{0}| = |I^{r}|, and imagine that a token is placed on each vertex in I0. The token jumping problem is to determine whether there exists a sequence of independent sets of the same cardinality which transforms I^{0} into I^{r} so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This problem is known to be PSPACE-complete even for planar graphs of maximum degree three, and W[1]-hard for general graphs when parameterized by the number of tokens. In this paper, we present a fixedparameter algorithm for token jumping on planar graphs, where the parameter is only the number of tokens. Furthermore, the algorithm can be modified so that it finds a shortest sequence for a yes-instance. The same scheme of the algorithms can be applied to a wider class of graphs which forbid a complete bipartite graph K^{3},t as a subgraph for a fixed integer t ≥ 3.

Original language | English |
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Title of host publication | Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings |

Editors | Hee-Kap Ahn, Chan-Su Shin |

Publisher | Springer Verlag |

Pages | 208-219 |

Number of pages | 12 |

ISBN (Electronic) | 9783319130743 |

DOIs | |

Publication status | Published - Jan 1 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8889 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings*(pp. 208-219). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8889). Springer Verlag. https://doi.org/10.1007/978-3-319-13075-0_17