COLORING OF THE dth POWER OF THE FACE-CENTERED CUBIC GRID
| Affiliation auteurs | Affiliation ok |
| Titre | COLORING OF THE dth POWER OF THE FACE-CENTERED CUBIC GRID |
| Type de publication | Journal Article |
| Year of Publication | 2021 |
| Auteurs | Gastineau N, Togni O |
| Journal | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
| Volume | 41 |
| Pagination | 1001-1020 |
| Type of Article | Article |
| ISSN | 1234-3099 |
| Mots-clés | distance coloring, dth power of graph, face-centered cubic grid |
| Résumé | 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. |
| DOI | 10.7151/dmgt.2257 |