# Extremal properties of flood-filling games

@article{Meeks2015ExtremalPO, title={Extremal properties of flood-filling games}, author={Kitty Meeks and Dominik K. Vu}, journal={Discret. Math. Theor. Comput. Sci.}, year={2015}, volume={21} }

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…

## 3 Citations

### A Survey on the Complexity of Flood-Filling Games

- EngineeringAdventures Between Lower Bounds and Higher Altitudes
- 2018

This survey, which reviews recent results on one-player flood-filling games on graphs, Flood-It and Free-Flood-It, in which the player aims to make the board monochromatic with a minimum number of flooding moves, has relevant interpretations in bioinformatics.

### How Bad is the Freedom to Flood-It?

- EngineeringFUN
- 2018

This paper investigates how freedom of choosing the vertex to play in each move affects the complexity of the problem, and shows that the length of an optimal solution for Fixed-Flood-It is always at most twice that of Free-Fl flooded, and this is tight.

### Vexing Vexillological Logic

- MathematicsArXiv
- 2022

We deﬁne a new impartial combinatorial game, flag coloring , based on ﬂood ﬁlling. We then generalize to a graph game, and ﬁnd values for many positions on two colors. We demonstrate that the…

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