Hat problem on graphs with exactly three cycles
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2022-10-23 21:28
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519.1 (106)
Analiză combinatorică. Teoria grafurilor (104)
SM ISO690:2012
BALEGH, Tayebe; RAD, NaderJafari. Hat problem on graphs with exactly three cycles. In: Computer Science Journal of Moldova. 2016, nr. 2(71), pp. 243-254. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 2(71) / 2016 / ISSN 1561-4042

Hat problem on graphs with exactly three cycles
CZU: 519.1

Pag. 243-254

Balegh Tayebe, Rad NaderJafari
University of Technology Shahrood
Disponibil în IBN: 2 septembrie 2016


This paper is devoted to investigation of the hat problem on graphs with exactly three cycles. In the hat problem, each of n players is randomly fitted with a blue or red hat. Everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player 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 winning. Note that every player can see everybody excluding himself. This problem has been considered on a graph, where the vertices correspond to the players, and a player can see each player to whom he is connected by an edge. We show that the hat number of a graph with exactly three cycles is 3/4 if it contains a triangle, and 1/2 otherwise.

Hat problem,