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.
Mathematics Subject Classification (2000)05C15 05C85
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- A. Hajnal and E. Szemerédi: Proof of a conjecture of P. Erdős, in: Combinatorial Theory and its Application (P. Erdős, A. Rényi and V. T. Sós, eds.), pp. 601–623, North-Holland, London, 1970.Google Scholar
- M. Mydlarz and E. Szemerédi: Algorithmic Brooks’ Theorem, manuscript.Google Scholar