The Flood-It game parameterized by the vertex cover number

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) con...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics 2015-12, Vol.50, p.35-40
Main Authors: Souza, Uéverton dos Santos, Rosamond, Frances, Fellows, Michael R., Protti, Fábio, Dantas da Silva, Maise
Format: Article
Language:English
Subjects:
fixed-parameter tractability
Flood-It
polynomial kernelization
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Summary: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.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2015.07.007