Geodesic
The pursuit-evasion game on the 1-skeleton graph of the regular polyhedron.~I
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 3-15

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We consider a game between a group of $n$ pursuers and one evader moving with the same maximal speed along 1-skeleton of a given regular polyhedron. The objective of the paper consists of finding an integer $N(M)$ possessing the following property: if $n \geq N(M)$ then the group of pursuers wins while if $n N(M)$ then an evader wins. Part I of the paper is devoted to the case of polyhedrons in the space $\mathbb{R}^N$, Part II will be devoted to the case $\mathbb{R}^N$, $n\geq5$, and Part III will be devoted to the case $\mathbb{R}^4$.
Keywords: pursuit-evasion game, approach problem, evasion problem, positional strategy, counterstrategy, exact catch, regular polyhedron, graph, one-dimensional graph. 
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     author = {Abdulla A. Azamov and Atamurat Sh. Kuchkarov and Azamat G. Holboyev},
     title = {The pursuit-evasion game on the 1-skeleton graph of the regular {polyhedron.~I}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/MGTA_2015_7_3_a0/}
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Abdulla A. Azamov; Atamurat Sh. Kuchkarov; Azamat G. Holboyev. The pursuit-evasion game on the 1-skeleton graph of the regular polyhedron.~I. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 3, pp. 3-15. http://geodesic.mathdoc.fr/item/MGTA_2015_7_3_a0/