### Abstract

Suppose that we are given two dominating sets D_{s} and D_{t} of a graph G whose cardinalities are at most a given threshold k. Then, we are asked whether there exists a sequence of dominating sets of G between D_{s} and D_{t} such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex. This decision problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by O(n), where n is the number of vertices in the input graph.

Original language | English |
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Title of host publication | Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Ulrike Stege |

Publisher | Springer Verlag |

Pages | 398-409 |

Number of pages | 12 |

ISBN (Print) | 9783319218397 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada Duration: Aug 5 2015 → Aug 7 2015 |

### 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 | 9214 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Symposium on Algorithms and Data Structures, WADS 2015 |
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Country | Canada |

City | Victoria |

Period | 8/5/15 → 8/7/15 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings*(pp. 398-409). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_33