Standard

Cliques and Constructors in “Hats” Game. II. / Kokhas, K. P.; Latyshev , A.S.; Retinskiy, V. I.

In: Journal of Mathematical Sciences (United States), Vol. 255, No. 1, 10.04.2021, p. 58-70.

Research output: Contribution to journal › Article › peer-review

Harvard

Kokhas, KP, Latyshev , AS & Retinskiy, VI 2021, 'Cliques and Constructors in “Hats” Game. II', Journal of Mathematical Sciences (United States), vol. 255, no. 1, pp. 58-70. https://doi.org/10.1007/s10958-021-05349-8

APA

Kokhas, K. P., Latyshev , A. S., & Retinskiy, V. I. (2021). Cliques and Constructors in “Hats” Game. II. Journal of Mathematical Sciences (United States), 255(1), 58-70. https://doi.org/10.1007/s10958-021-05349-8

Vancouver

Kokhas KP, Latyshev AS, Retinskiy VI. Cliques and Constructors in “Hats” Game. II. Journal of Mathematical Sciences (United States). 2021 Apr 10;255(1):58-70. https://doi.org/10.1007/s10958-021-05349-8

Author

Kokhas, K. P. ; Latyshev , A.S. ; Retinskiy, V. I. / Cliques and Constructors in “Hats” Game. II. In: Journal of Mathematical Sciences (United States). 2021 ; Vol. 255, No. 1. pp. 58-70.

BibTeX

@article{5c8a22fcacff418ab8dd75fefe7eb5f2,
title = "Cliques and Constructors in “Hats” Game. II",
abstract = "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. Winning strategies for the sages on complete graphs are demonstrated, and the Hats games on almost complete graphs are analyzed. Several theorems demonstrating how one can construct new graphs for which the sages win are proved.",
author = "Kokhas, {K. P.} and A.S. Latyshev and Retinskiy, {V. I.}",
note = "Publisher Copyright: {\textcopyright} 2021, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2021",
month = apr,
day = "10",
doi = "10.1007/s10958-021-05349-8",
language = "English",
volume = "255",
pages = "58--70",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Cliques and Constructors in “Hats” Game. II

AU - Kokhas, K. P.

AU - Latyshev , A.S.

AU - Retinskiy, V. I.

N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/4/10

Y1 - 2021/4/10

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. Winning strategies for the sages on complete graphs are demonstrated, and the Hats games on almost complete graphs are analyzed. Several theorems demonstrating how one can construct new graphs for which the sages win are proved.

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. Winning strategies for the sages on complete graphs are demonstrated, and the Hats games on almost complete graphs are analyzed. Several theorems demonstrating how one can construct new graphs for which the sages win are proved.

UR - http://www.scopus.com/inward/record.url?scp=85104268357&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4cdda29c-1a26-366c-bc4c-fc77ae7a6de6/

U2 - 10.1007/s10958-021-05349-8

DO - 10.1007/s10958-021-05349-8

M3 - Article

AN - SCOPUS:85104268357

VL - 255

SP - 58

EP - 70

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 86150479