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It is shown that the maximum possible chromatic number of the square of a graph with maximum degree d and girth g is (1 + o (1)) d 2 if g = 3, 4, 5 or 6, and is Θ( d 2 / log d ) if g [ges ] 7. Extensions to higher powers are considered as well.
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Alon et al. (2002) studied this question.
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