### Chong Shangguan (上官冲), The hat guessing number of graphs

### Chong Shangguan (上官冲), The hat guessing number of graphs

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 not his own hat color. All of the players are asked to …