Coloration des graphes de reines

Until 2003 no chromatic numbers (${\chi }_n$) for the queen graphs were available for $n>9$ except where n is not a multiple of 2 or 3. In this research announcement we present an exact algorithm which provides coloring solutions for $n=12,14,15,16,18,20,21,22,24,26,28$ and 32 such as ${\chi }_n=n$. Then we prove that there exists an infinite number of values for n such that $n=2p$ or $n=3p$, and ${\chi }_n=n$. To cite this article: M. Vasquez, C. R. Acad. Sci. Paris, Ser. I 342 (2006).