# On Complexity of Flooding Games on Graphs with Interval Representations

@inproceedings{Fukui2012OnCO, title={On Complexity of Flooding Games on Graphs with Interval Representations}, author={Hiroyuki Fukui and Yota Otachi and Ryuhei Uehara and Takeaki Uno and Yushi Uno}, booktitle={TJJCCGG}, year={2012} }

The flooding games, which are called Flood-It, Mad Virus, or HoneyBee, are a kind of coloring games and they have been becoming popular online. In these games, each player colors one specified cell in his/her turn, and all connected neighbor cells of the same color are also colored by the color. This flooding or coloring spreads on the same color cells. It is natural to consider the coloring games on general graphs: Once a vertex is colored, the flooding flows along edges in the graph. Recently…

## 8 Citations

### N ov 2 01 5 Flood-it on AT-Free Graphs

- Computer Science
- 2018

It is shown that the minimal number of moves can be computed in polynomial time when the game is played on AT-free graphs.

### Flood-it on AT-Free Graphs

- Computer ScienceArXiv
- 2015

It is shown that the minimal number of moves can be computed in polynomial time when the game is played on AT-free graphs.

### Extremal properties of flood-filling games

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2019

This work begins a systematic investigation of the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It, and determines the maximum number of moves that may be required, taken over all possible colourings.

### 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.

### Twenty Years of Progress of ${JCDCG}^3$

- BiologyGraphs Comb.
- 2020

A summary of the notable results published in those proceedings are presented in this article and focus on six areas such as games and puzzles, dissection and reversibility, foldings and unfoldings, point sets, visibility, and geometric and topological graph theory.

### Twenty Years of Progress of JCDCG3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {JCDCG}^3$$\end{document}

- Graphs and Combinatorics
- 2020

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Two polynomial-time algorithms for flood-filling problems related to the combinatorial game (Free-) Flood-It are considered, which show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over all spanning trees T of G, of the number of Moves to flood T.

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