Hat problem on graphs with exactly three cycles
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 tea...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vladimir Andrunachievici Institute of Mathematics and Computer Science
2016-08-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v24-n2/v24-n2-(pp243-254).pdf |
| _version_ | 1811184907403132928 |
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| author | Tayebe Balegh Nader Jafari Rad |
| author_facet | Tayebe Balegh Nader Jafari Rad |
| author_sort | Tayebe Balegh |
| collection | DOAJ |
| description | 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 $\frac{3}{4}$ if it contains a triangle, and $\frac{1}{2}$ otherwise. |
| first_indexed | 2024-04-11T13:21:32Z |
| format | Article |
| id | doaj.art-6e0a1bc8ba3c4a6b9d67c1a20f517fd2 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-11T13:21:32Z |
| publishDate | 2016-08-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-6e0a1bc8ba3c4a6b9d67c1a20f517fd22022-12-22T04:22:12ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422016-08-01242(71)243254Hat problem on graphs with exactly three cyclesTayebe BaleghNader Jafari Rad0Department of Mathematics, Shahrood University of Technology, Shahrood, IranThis 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 $\frac{3}{4}$ if it contains a triangle, and $\frac{1}{2}$ otherwise.http://www.math.md/files/csjm/v24-n2/v24-n2-(pp243-254).pdfHat problemStrategy |
| spellingShingle | Tayebe Balegh Nader Jafari Rad Hat problem on graphs with exactly three cycles Computer Science Journal of Moldova Hat problem Strategy |
| title | Hat problem on graphs with exactly three cycles |
| title_full | Hat problem on graphs with exactly three cycles |
| title_fullStr | Hat problem on graphs with exactly three cycles |
| title_full_unstemmed | Hat problem on graphs with exactly three cycles |
| title_short | Hat problem on graphs with exactly three cycles |
| title_sort | hat problem on graphs with exactly three cycles |
| topic | Hat problem Strategy |
| url | http://www.math.md/files/csjm/v24-n2/v24-n2-(pp243-254).pdf |
| work_keys_str_mv | AT tayebebalegh hatproblemongraphswithexactlythreecycles AT naderjafarirad hatproblemongraphswithexactlythreecycles |