Geodesic
Search problems on graphs of regular polyhedra
Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 108-116 
N. N. Petrov. Search problems on graphs of regular polyhedra. Diskretnaya Matematika, Tome 8 (1996) no. 2, pp. 108-116. http://geodesic.mathdoc.fr/item/DM_1996_8_2_a7/
@article{DM_1996_8_2_a7,
     author = {N. N. Petrov},
     title = {Search problems on graphs of regular polyhedra},
     journal = {Diskretnaya Matematika},
     pages = {108--116},
     year = {1996},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_2_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the $n$-search number of a graph which is defined as the minimal number of pursuers needed to catch a moving object on a connected graph provided that there are no constraints on their velocity; $n$ characterizes the required closeness of the pursuers to the evader. We give the $n$-search numbers for the graphs of all regular polyhedra.