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Automation and Remote Control

, Volume 80, Issue 1, pp 164–170 | Cite as

The Pursuit-Evasion Game on the 1-Skeleton Graph of a Regular Polyhedron. II

  • A. A. AzamovEmail author
  • A. Sh. Kuchkarov
  • A. G. Holboyev
Mathematical Game Theory and Applications
  • 3 Downloads

Abstract

Part II of the paper considers a game between a group of n pursuers and one evader that move along the 1-Skeleton graph M of regular polyhedrons of three types in the spaces ℝd, d ≥ 3. Like in Part I, the goal is to find an integer N(M) with the following property: if nN(M), then the group of pursuers wins the game; if n < N(M), the evader wins. It is shown that N(M) = 2 for the d-dimensional simplex or cocube (a multidimensional analog of octahedron) and N(M) = [d/2] + 1 for the d-dimensional cube.

Keywords

pursuit-evasion game approach problem evasion problem positional strategy counterstrategy exact capture regular polyhedron one-dimensional skeleton graph 

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References

  1. 1.
    Azamov, A.A., Kuchkarov, A.Sh., and Holboev, A.G., The Pursuit-Evasion Game on the 1-Skeleton Graph of a Regular Polyhedron. I, Autom. Remote Control, 2017, vol. 78, no. 4, pp. 754–761.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berger, M., Geometry. Volume 1, Berlin: Springer-Verlag, 1987.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • A. A. Azamov
    • 1
    Email author
  • A. Sh. Kuchkarov
    • 1
    • 2
  • A. G. Holboyev
    • 2
  1. 1.Institute of Mathematics of the National University of UzbekistanTashkentUzbekistan
  2. 2.Tashkent Institute of Architecture and Civil EngineeringTashkentUzbekistan

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