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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics