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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2023, Volume 15, Issue 3, Pages 3–20 (Mi mgta333)  
Police and robber game on infinite chessboard

Abdulla A. Azamova, Fatxull À. Êuvatovb, Hasan U. Tuyliyevb

a Institute of Mathematics, Uzbekistan Akademy of Science
b National University of Uzbekistan
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Abstract: It is considered two variants of the game "Policeman and a robber" on an infinite chessboard that is a graph giving a regular partition of the plane into squares. Heuristic and precise definitions of the concepts "the initial state is winning for the pursuer" and "the initial state is winning for the evader" are formulated. Then, criteria for determining if a given initial state is winning for the pursuer or for the evader is given.
Keywords: game on graphs, integere net, "Cops$\&$Robber" game, qualitative problem, pursuit problem, evading problem, strategy, alternative.
Received: 27.01.2023
Revised: 15.03.2023
Accepted: 30.03.2023
Document Type: Article
UDC: 517.97
BBC: 22.18
Language: Russian
Citation: Abdulla A. Azamov, Fatxull À. Êuvatov, Hasan U. Tuyliyev, “Police and robber game on infinite chessboard”, Mat. Teor. Igr Pril., 15:3 (2023), 3–20
Citation in format AMSBIB
\Bibitem{AzaÊuvTuy23}
\by Abdulla~A.~Azamov, Fatxull~À.~Êuvatov, Hasan~U.~Tuyliyev
\paper Police and robber game on infinite chessboard
\jour Mat. Teor. Igr Pril.
\yr 2023
\vol 15
\issue 3
\pages 3--20
\mathnet{http://mi.mathnet.ru/mgta333}
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