### Abstract

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn^{2}) time, where n is the number of vertices.

Original language | English (US) |
---|---|

Pages (from-to) | 217-224 |

Number of pages | 8 |

Journal | Combinatorica |

Volume | 30 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics

### Cite this

*Combinatorica*,

*30*(2), 217-224. https://doi.org/10.1007/s00493-010-2483-5

**A fast algorithm for equitable coloring.** / Kierstead, Henry; Kostochka, Alexandr V.; Mydlarz, Marcelo; Szemerédi, Endre.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 30, no. 2, pp. 217-224. https://doi.org/10.1007/s00493-010-2483-5

}

TY - JOUR

T1 - A fast algorithm for equitable coloring

AU - Kierstead, Henry

AU - Kostochka, Alexandr V.

AU - Mydlarz, Marcelo

AU - Szemerédi, Endre

PY - 2010

Y1 - 2010

N2 - A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn2) time, where n is the number of vertices.

AB - A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn2) time, where n is the number of vertices.

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U2 - 10.1007/s00493-010-2483-5

DO - 10.1007/s00493-010-2483-5

M3 - Article

AN - SCOPUS:77956970690

VL - 30

SP - 217

EP - 224

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 2

ER -