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A Cop and Drunken Robber Game on n -Dimensional Infinite-Grid Graphs

Author

Listed:
  • Nuttanon Songsuwan

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Thiradet Jiarasuksakun

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Anuwat Tangthanawatsakul

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Mathematics and Statistics with Applications (MaSA), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Pawaton Kaemawichanurat

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Mathematics and Statistics with Applications (MaSA), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

Abstract

A Cop and Drunken Robber (CDR) game is one variation of a famous combinatorial game, called Cops and Robbers, which has been extensively studied and applied in the area of theoretical and computer science as demonstrated by several conferences and publications. In this paper, for a natural number n , we present two strategies for a single cop to chase a drunken robber on n -dimensional infinite-grid graphs. Both strategies show that if the initial distance between the cop and the drunken robber is s , then the expected capture time is s + o ( s ) .

Suggested Citation

  • Nuttanon Songsuwan & Thiradet Jiarasuksakun & Anuwat Tangthanawatsakul & Pawaton Kaemawichanurat, 2021. "A Cop and Drunken Robber Game on n -Dimensional Infinite-Grid Graphs," Mathematics, MDPI, vol. 9(17), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2107-:d:626410
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