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The face-centered cubic grid is a three dimensional 12-regular infinite grid.This graph represents an optimal way to pack spheres in the three-dimensionalspace. In this grid, the vertices represent the spheres and the edges representthe contact between spheres. We give lower and upper bounds on the chromaticnumber of the d th power of the face-centered cubic grid. In particular, in thecase d = 2 we prove that the chromatic number of this grid is 13. We alsodetermine sharper bounds for d = 3 and for subgraphs of of the face-centeredcubic grid.

Coloring of the dth power of the face-centered cubic grid