Geodesic
Police and robber game on infinite chessboard
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 3, pp. 3-20

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MGTA_2023_15_3_a0,
     author = {Abdulla A. Azamov and Fatxull {\CYRA}. {\CYRK}uvatov and Hasan U. Tuyliyev},
     title = {Police and robber game on infinite chessboard},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2023_15_3_a0/}
}
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Abdulla A. Azamov; Fatxull А. Кuvatov; Hasan U. Tuyliyev. Police and robber game on infinite chessboard. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 3, pp. 3-20. http://geodesic.mathdoc.fr/item/MGTA_2023_15_3_a0/