### Abstract

For an integer k 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k 4, and solvable for any graph in polynomial time if k 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color and each edge in R represents a pair of colors that can be recolored directly. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle.

Original language | English |
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Title of host publication | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |

Editors | Takeshi Tokuyama, Yoshio Okamoto |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770545 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

Event | 28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand Duration: 2017 Dec 9 → 2017 Dec 22 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 92 |

ISSN (Print) | 1868-8969 |

### Other

Other | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |
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Country | Thailand |

City | Phuket |

Period | 17/12/9 → 17/12/22 |

### Keywords

- Combinatorial reconfiguration
- Graph coloring
- Pspace-complete

### ASJC Scopus subject areas

- Software

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## Cite this

*28th International Symposium on Algorithms and Computation, ISAAC 2017*(Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.62