Geodesic
Balanced Graph Partitions
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 127-133

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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 $r$. 
@article{MZM_2006_79_1_a10,
     author = {K. D. Protasova},
     title = {Balanced {Graph} {Partitions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {127--133},
     publisher = {mathdoc},
     volume = {79},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a10/}
}
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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/