### Abstract

Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. Each hat can have one of three colors. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We completely solve the problem of describing all graphs for which the sages win.

Original language | English |
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Journal | Journal of Mathematical Sciences (United States) |

Volume | 236 |

Issue number | 5 |

DOIs | |

Publication status | Accepted/In press - 1 Jan 2018 |

### Fingerprint

### Scopus subject areas

- Mathematics(all)
- Statistics and Probability
- Applied Mathematics

### Cite this

*Journal of Mathematical Sciences (United States)*,

*236*(5). https://doi.org/10.1007/s10958-018-4128-y

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*Journal of Mathematical Sciences (United States)*, vol. 236, no. 5. https://doi.org/10.1007/s10958-018-4128-y

**For Which Graphs the Sages Can Guess Correctly the Color of at Least One Hat.** / Kokhas, K.; Latyshev, A.

Research output

TY - JOUR

T1 - For Which Graphs the Sages Can Guess Correctly the Color of at Least One Hat

AU - Kokhas, K.

AU - Latyshev, A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. Each hat can have one of three colors. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We completely solve the problem of describing all graphs for which the sages win.

AB - Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. Each hat can have one of three colors. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We completely solve the problem of describing all graphs for which the sages win.

UR - http://www.scopus.com/inward/record.url?scp=85058455121&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-4128-y

DO - 10.1007/s10958-018-4128-y

M3 - Article

AN - SCOPUS:85058455121

VL - 236

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -