Related papers: Hat chromatic number of graphs

The hat guessing number $HG(G)$ of a graph $G$ on $n$ vertices is defined in terms of the following game: $n$ players are placed on the $n$ vertices of $G$, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible…

We analyze the following version of the deterministic \hats game. We have a graph $G$, and a sage resides at each vertex of $G$. When the game starts, an adversary puts on the head of each sage a hat of a color arbitrarily chosen from a set…

Consider the following hat guessing game: $n$ players are placed on $n$ vertices of a graph, each wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but…

Let $G$ be a graph with $n$ vertices. The {\em hat guessing number} of $G$ is defined in terms of the following game: There are $n$ players and one opponent. The opponent will wear one of the $q$ hats of different colors on the player's…

We study the hat guessing game on graphs. In this game, a player is placed on each vertex $v$ of a graph $G$ and assigned a colored hat from $h(v)$ possible colors. Each player makes a deterministic guess on their hat color based on the…

A team of players plays the following game. After a strategy session, each player is randomly fitted with a blue or red hat. Then, without further communication, everybody can try to guess simultaneously his or her own hat color by looking…

Assume $n$ players are placed on the $n$ vertices of a graph $G$. The following game was introduced by Winkler: An adversary puts a hat on each player, where each hat has a colour out of $q$ available colours. The players can see the hat of…

We consider the following game, played on a $k$-uniform hypergraph $H$. There are $q$ colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to…

Consider the following hat guessing game. A bear sits on each vertex of a graph $G$, and a demon puts on each bear a hat colored by one of $h$ colors. Each bear sees only the hat colors of his neighbors. Based on this information only, each…

Suppose that two players take turns coloring the vertices of a given graph G with k colors. In each move the current player colors a vertex such that neighboring vertices get different colors. The first player wins this game if and only if…

N players are randomly fitted with a colored hat (q different colors). All players guess simultaneously the color of their own hat observing only the hat colors of the other N-1 players. The team wins if all players guess right. No…

Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are…

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,…

Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbours without exchanging any information. Each hat can have one of…

We consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and the other player attempting to prevent a proper coloring.…

We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of $k$ colors. Each sage tries to guess the color of his own hat…

The following general variant of deterministic Hats game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the $k$-th sage can have hats of one of $h(k)$ colors. Each sage tries to guess the color of his own…

In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…

Game coloring is a well-studied two-player game in which each player properly colors one vertex of a graph at a time until all the vertices are colored. An `eternal' version of game coloring is introduced in this paper in which the vertices…

We initiate the study of the hat guessing number of a graph where the adversary is only allowed to provide a proper coloring of the graph. This is the largest number $q$ for which there is a guessing strategy on each vertex that only…