The Flood-It game parameterized by the vertex cover number

U.D.S. Souza, Frances Rosamond, Michael Fellows, Fabio Protti, Maise Dantas da Silva

    Research output: Contribution to journalArticle

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)35-40
    Number of pages6
    JournalElectronic Notes in Discrete Mathematics
    Volume50
    DOIs
    Publication statusPublished - Dec 2015

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