Hat problem on some graphs

Suppose that there is a team of n people each israndomly fitted with a blue or red hat. Everybody can try toguess simultanously his own hat color looking at the hat colorsof the other people. The team wins if at least one person guesseshis hat color correctly and no one guesses his hat color wrong,otherwise the team loses. The aim is to maximize the probabilityof winning. Note that every person can see everybody excludinghim. This problem has been considered on a graph, where thevertices are people, and a person can see those people to whichhe is connected by an edge. The solution of the hat problem isknown for trees, paths and some of cycles. In this talk we wishto solve the problem on the corona graph over C4 in details.