Abstract
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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References
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.
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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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DOI: https://doi.org/10.1007/s11006-006-0011-0