We prove that the set of vertices V, |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.
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J. Karaganis, “On the cube of graphs,” Canad. Math. Bull., 11 (1969), 295–296.
K. D. Protasova, “Kaleidoscopic graphs,” Math. Stud., 18 (2002), 3–9.
Translated from Matematicheskie Zametki, vol. 79, no. 1, 2006, pp. 127–133.
Original Russian Text Copyright © 2006 by K. D. Protasova.
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Protasova, K.D. Balanced Graph Partitions. Math Notes 79, 116–121 (2006). https://doi.org/10.1007/s11006-006-0011-0
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