Coloring of the d th Power of the Face-Centered Cubic Grid
Nicolas Gastineau, Togni Olivier · DOAJ (DOAJ: Directory of Open Access Journals) · 2021
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-dimensional space. We give lower and upper bounds on the chromatic number of the dth power of the face-centered cubic grid. In particular, in the case d = 2 we prove that the chromatic number of this grid is 13. We also determine sharper bounds for d = 3 and for subgraphs of the face-centered cubic grid.