Geodesic
Balanced Graph Partitions
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 127-133 
K. D. Protasova. Balanced Graph Partitions. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 127-133. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a10/
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     author = {K. D. Protasova},
     title = {Balanced {Graph} {Partitions}},
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     volume = {79},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the set of vertices $\mathscr V$, $|\mathscr V|=rk$, of a connected graph $G$ can be split into $r$ subsets of the same cardinality in such a way that the distance between any vertex of $G$ and any subset of the partition is at most $r$.

[1] Karaganis J., “On the cube of graphs”, Canad. Math. Bull., 11 (1969), 295–296 | MR

[2] Protasova K. D., “Kaleidoscopic graphs”, Math. Stud., 18 (2002), 3–9 | MR | Zbl