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Cliques and Constructors in “Hats” Game. I. / Kokhas, K.; Latyshev, A.
в: Journal of Mathematical Sciences (United States), Том 255, № 1, 12.04.2021, стр. 39-57.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Cliques and Constructors in “Hats” Game. I
AU - Kokhas, K.
AU - Latyshev, A.
N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/4/12
Y1 - 2021/4/12
N2 - The following general variant of deterministic “Hats” game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the kth sage can have hats of one of h(k) colors. 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. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. For complete graphs and cycles, the problem of describing the function h(k) for which the sages win is solved in the present paper. A “theory of constructors,” i.e., a collection of theorems demonstrating how one can construct new graphs for which the sages win is developed. A new game “Rook check ” equivalent to the Hats game on a 4-cycle is introduced and completely analyzed.
AB - The following general variant of deterministic “Hats” game is analyzed. Several sages wearing colored hats occupy the vertices of a graph, the kth sage can have hats of one of h(k) colors. 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. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. For complete graphs and cycles, the problem of describing the function h(k) for which the sages win is solved in the present paper. A “theory of constructors,” i.e., a collection of theorems demonstrating how one can construct new graphs for which the sages win is developed. A new game “Rook check ” equivalent to the Hats game on a 4-cycle is introduced and completely analyzed.
UR - http://www.scopus.com/inward/record.url?scp=85104376924&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/cf5bf31d-cd29-3ecb-b5e6-c46c99f6984c/
U2 - 10.1007/s10958-021-05348-9
DO - 10.1007/s10958-021-05348-9
M3 - Article
AN - SCOPUS:85104376924
VL - 255
SP - 39
EP - 57
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 1
ER -
ID: 86150411