区间表示图上泛洪博弈的复杂性
On Complexity of Flooding Games on Graphs with Interval Representations
摘要：
洪水游戏，这是所谓的洪水，它，疯狂的病毒，或蜜蜂，是一种着色游戏，他们已经成为流行的在线。在这些游戏中，每个玩家在他/她的回合中给一个指定的细胞着色，并且所有相同颜色的连接的相邻细胞也被颜色着色。这种泛色或着色在相同颜色的细胞上扩散。在更一般的棋盘或一般的图上考虑这些新的着色游戏是很自然的。近年来，人们研究了几类图上泛洪对策的变种的计算复杂性。本文研究了一类具有区间表示的图类上的洪泛对策。我们的研究结果表明，颜色的数量是一个关键参数，以确定计算复杂性的洪水游戏。当颜色数为固定常数时，这些博弈可以在区间图上用多项式时间求解。另一方面，如果颜色的数量是没有界的，洪水游戏是NP-完全的适当的区间图。我们也状态分裂图类似的结果。
英文摘要：
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 these new coloring games on more general boards, or general graphs. Recently, computational complexities of the variants of the flooding games on several graph classes have been studied. In this paper, we investigate the flooding games on some graph classes characterized by interval representations. Our results state that the number of colors is a key parameter to determine the computational complexity of the flooding games. When the number of colors is a fixed constant, these games can be solved in polynomial time on an interval graph. On the other hand, if the number of colors is not bounded, the flooding game is NP-complete on a proper interval graph. We also state similar results for split graphs.
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