Geodesic
Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games
Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 145-159

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We study conditions for the existence of coalition games with the result invariant under cyclic shifts of players sequence numbers. Given a total number $ n $ of players, we estimate the number $ k $ of players of one coalition under which there exists a game in which this coalition wins under all cyclic shifts of players. We give procedures for construction of the so-called set-splitting digraphs on which risk-free nim-type games of a given coalition are defined.
Keywords: positional game, risk-free game, cyclic sequence, difference set. 
@article{DM_2016_28_3_a9,
     author = {A. M. Chudnov},
     title = {Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games},
     journal = {Diskretnaya Matematika},
     pages = {145--159},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_3_a9/}
}
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A. M. Chudnov. Cyclic decomposition of sets, set-splitting digraphs and cyclic classes of risk-free games. Diskretnaya Matematika, Tome 28 (2016) no. 3, pp. 145-159. http://geodesic.mathdoc.fr/item/DM_2016_28_3_a9/