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The achromatic number of a nite graph G, (G), is the maximum number of independent sets into which the vertex set may be partitioned, so that between any two parts there is at least one edge. For an m-dimensional hypercube P m 2 we prove: There exist constants 0 < c 1 < c 2 , independent of m, such that c 1 (m2 m?1 ) 1=2 (P m 2 ) c 2 (m2 m?1 ) 1=2 :doi:10.1006/jctb.2000.1955 fatcat:fg6cticnzzeg3fjydmlnv3znfy