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The topic of our paper is the hat problem. In that problem, each of n people is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color looking at the hat colors of the other people. The team wins if at least one person guesses his hat color correctly and no one guesses his hat color wrong, otherwise the team loses. The aim is to maximize the probability of win. In this version every person can see everybody excluding him. In this paper we consider such problem on a graph, where vertices are people and a person can see these people, to which he is connected by an edge. We prove some general theorems about the hat problem on a graph and solve the problem on trees. We also consider the hat problem on a graph with given degrees of vertices. We give an upper bound that is based only on the degrees of vertices on the chance of success of any strategy for the graph G. We show that this upper bound together with integrality constraints is tight on some toy examples.
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- Kategoria:
- Publikacja w czasopiśmie
- Typ:
- artykuły w czasopismach recenzowanych i innych wydawnictwach ciągłych
- Opublikowano w:
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Mathematica Pannonica
nr 21,
strony 3 - 21,
ISSN: 0865-2090 - Język:
- angielski
- Rok wydania:
- 2010
- Opis bibliograficzny:
- Krzywkowski M.: Hat problem on a graph// Mathematica Pannonica. -Vol. 21., iss. 1 (2010), s.3-21
- Weryfikacja:
- Politechnika Gdańska
wyświetlono 99 razy