### Abstract

Original language | English |
---|---|

Pages (from-to) | 35-40 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 50 |

DOIs | |

Publication status | Published - Dec 2015 |

### Fingerprint

### Cite this

*Electronic Notes in Discrete Mathematics*,

*50*, 35-40. https://doi.org/10.1016/j.endm.2015.07.007

}

*Electronic Notes in Discrete Mathematics*, vol. 50, pp. 35-40. https://doi.org/10.1016/j.endm.2015.07.007

**The Flood-It game parameterized by the vertex cover number.** / Souza, U.D.S.; Rosamond, Frances; Fellows, Michael; Protti, Fabio; Dantas da Silva, Maise.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The Flood-It game parameterized by the vertex cover number

AU - Souza, U.D.S.

AU - Rosamond, Frances

AU - Fellows, Michael

AU - Protti, Fabio

AU - Dantas da Silva, Maise

PY - 2015/12

Y1 - 2015/12

N2 - Flood-It is a combinatorial problem on a colored graph whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a pivot vertex p. A flooding move consists of changing the color of the monochromatic component (maximal monochromatic connected subgraph) containing p. This problem generalizes a combinatorial game named alike which is played on m×n grids. It is known that Flood-It remains NP-hard even for 3×n grids and for instances with bounded number of colors, diameter, or treewidth. In contrast, in this work we show that Flood-It is fixed-parameter tractable when parameterized by the vertex cover number, and admits a polynomial kernelization when, besides the vertex cover number, the number of colors is an additional parameter.

AB - Flood-It is a combinatorial problem on a colored graph whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a pivot vertex p. A flooding move consists of changing the color of the monochromatic component (maximal monochromatic connected subgraph) containing p. This problem generalizes a combinatorial game named alike which is played on m×n grids. It is known that Flood-It remains NP-hard even for 3×n grids and for instances with bounded number of colors, diameter, or treewidth. In contrast, in this work we show that Flood-It is fixed-parameter tractable when parameterized by the vertex cover number, and admits a polynomial kernelization when, besides the vertex cover number, the number of colors is an additional parameter.

U2 - 10.1016/j.endm.2015.07.007

DO - 10.1016/j.endm.2015.07.007

M3 - Article

VL - 50

SP - 35

EP - 40

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

SN - 1571-0653

ER -