Extremal properties of flood-filling games

Meeks, K. and Vu, D. K. (2019) Extremal properties of flood-filling games. Discrete Mathematics and Theoretical Computer Science, 21(4), 12. (doi: 10.23638/DMTCS-21-4-11)

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The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required, taken over all possible colourings. We give several upper and lower bounds on this quantity for arbitrary graphs and show that all of the bounds are tight for trees; we also investigate how much the upper bounds can be improved if we restrict our attention to graphs with higher edge-density.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Meeks, Dr Kitty
Authors: Meeks, K., and Vu, D. K.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Discrete Mathematics and Theoretical Computer Science
ISSN (Online):1365-8050
Copyright Holders:Copyright © 2019 The Authors
First Published:First published in Discrete Mathematics and Theoretical Computer Science 21(4):12
Publisher Policy:Reproduced under a Creative Commons License

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