The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. II
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 3-13
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Part II of the paper considers a game between a group of $n$ pursuers and one evader that move along the $1$-Skeleton graph $\mathbf{M}$ of regular polyhedrons of three types in the spaces $\mathbb{R}^d$, $d\geqslant 3$. Like in Part I, the goal is to find an integer $N(\mathbf{M})$ with the following property: if $n\geqslant N(\mathbf{M})$, then the group of pursuers wins the game; if $n$, the evader wins. It is shown that $N(\mathbf{M})=2$ for the $d$-dimensional simplex or cocube (a multidimensional analog of octahedron) and $N(\mathbf{M})=[d/2]+1$ for the $d$-dimensional cube.
Keywords:
pursuit-evasion game, approach problem, evasion problem, positional strategy, counterstrategy, exact capture, regular polyhedron, one-dimensional skeleton, graph.
@article{MGTA_2016_8_4_a0,
author = {Abdulla A. Azamov and Atamurat Sh. Kuchkarov and Azamat G. Holboyev},
title = {The pursuit-evasion game on the 1-skeleton graph of a regular {polyhedron.~II}},
journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
pages = {3--13},
year = {2016},
volume = {8},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a0/}
}
TY - JOUR AU - Abdulla A. Azamov AU - Atamurat Sh. Kuchkarov AU - Azamat G. Holboyev TI - The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. II JO - Matematičeskaâ teoriâ igr i eë priloženiâ PY - 2016 SP - 3 EP - 13 VL - 8 IS - 4 UR - http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a0/ LA - ru ID - MGTA_2016_8_4_a0 ER -
%0 Journal Article %A Abdulla A. Azamov %A Atamurat Sh. Kuchkarov %A Azamat G. Holboyev %T The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. II %J Matematičeskaâ teoriâ igr i eë priloženiâ %D 2016 %P 3-13 %V 8 %N 4 %U http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a0/ %G ru %F MGTA_2016_8_4_a0
Abdulla A. Azamov; Atamurat Sh. Kuchkarov; Azamat G. Holboyev. The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. II. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 8 (2016) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/MGTA_2016_8_4_a0/
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