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首页> 外文期刊>SIAM Journal on Discrete Mathematics >NEW CONSTRUCTIONS AND BOUNDS FOR WINKLER'S HAT GAME
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NEW CONSTRUCTIONS AND BOUNDS FOR WINKLER'S HAT GAME

机译：温克勒帽子游戏的新结构和新界限

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摘要

Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game, introduced by Winkler and studied by Butler et al. A team is composed of several players; each player is assigned a hat of a given color; they do not see their own color but can see some other hats, according to a directed graph. The team wins if they have a strategy such that, for any possible assignment of colors to their hats, at least one player guesses their own hat color correctly. In this paper, we discover some new classes of graphs which allow a winning strategy, thus answering some of the open questions of Butler et al. We also derive upper bounds on the maximal number of possible hat colors that allow for a winning strategy for a given graph.
机译：帽子问题最近已成为组合数学和离散数学的热门话题。这些已被证明与编码理论，网络编码和拍卖紧密相关。我们考虑由Winkler引入并由Butler等人研究的帽子游戏的以下版本。一个团队由几个球员组成；为每个玩家分配一顶给定颜色的帽子；根据有向图，他们看不到自己的颜色，但可以看到其他帽子。如果球队拥有这样的策略获胜，那么至少要有一名球员正确猜出自己的帽子颜色，这样才能对帽子进行颜色分配。在本文中，我们发现了一些新类别的图，这些图允许获胜策略，从而回答了Butler等人的一些未解决的问题。我们还得出了可能的帽子颜色最大数量的上限，该上限允许给定图形的获胜策略。

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