Skip to main content

Balanced Graph Partitions


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.

This is a preview of subscription content, access via your institution.


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

    MathSciNet  Google Scholar 

  2. K. D. Protasova, “Kaleidoscopic graphs,” Math. Stud., 18 (2002), 3–9.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information


Translated from Matematicheskie Zametki, vol. 79, no. 1, 2006, pp. 127–133.

Original Russian Text Copyright © 2006 by K. D. Protasova.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Protasova, K.D. Balanced Graph Partitions. Math Notes 79, 116–121 (2006).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Key words

  • balanced graph coloring
  • diameter of a graph
  • star graph
  • balanced partition
  • spanning tree
  • r-critical tree
  • Cayley graph