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

K. Kokhas, A. Latyshev

Research output

1 Citation (Scopus)

### 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 Journal of Mathematical Sciences (United States) 236 5 https://doi.org/10.1007/s10958-018-4128-y Accepted/In press - 1 Jan 2018

### Fingerprint

Guess
Color
Graph in graph theory
Assignment
Vertex of a graph

### Scopus subject areas

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

### Cite this

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title = "For Which Graphs the Sages Can Guess Correctly the Color of at Least One Hat",
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.",
author = "K. Kokhas and A. Latyshev",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/s10958-018-4128-y",
language = "English",
volume = "236",
journal = "Journal of Mathematical Sciences",
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publisher = "Springer",
number = "5",

}

In: Journal of Mathematical Sciences (United States), Vol. 236, No. 5, 01.01.2018.

Research output

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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.

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JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

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