A correction to Brelaz's modification of Brown's coloring algorithm
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Brelaz's modification of Brown's exact coloring algorithm contains two errors as demonstrated in two examples. A correct version of the algorithm and a proof of the exactness are given. Finally, Brown's look-ahead rule is built into this algorithm.
[1] Daniel Brélaz,et al. New methods to color the vertices of a graph , 1979, CACM.
[2] J. R. Brown. Chromatic Scheduling and the Chromatic Number Problem , 1972 .