### Abstract

A proper vertex colouring of a graph is equitable if the sizes of colour classes differ by at most one. We present a new shorter proof of the celebrated Hajnal-Szemerédi theorem: for every positive integer r, every graph with maximum degree at most r has an equitable colouring with r + 1 colours. The proof yields a polynomial time algorithm for such colourings.

Original language | English (US) |
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Pages (from-to) | 265-270 |

Number of pages | 6 |

Journal | Combinatorics Probability and Computing |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2008 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

Kierstead, H., & Kostochka, A. V. (2008). A short proof of the Hajnal-Szemerédi theorem on equitable colouring.

*Combinatorics Probability and Computing*,*17*(2), 265-270. https://doi.org/10.1017/S0963548307008619