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arXiv · 1510.08168

On two $q$-ary $n$-cube coloring problems

Z. Han·M. Lu
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Abstract

Let $χ'_d(n,q)$ (resp. $χ_d(n,q)$) denote the minimum number of colors necessary to color a $q$-ary $n$-cube so that no two vertices that are at a distance at most $d$ (resp. exactly $d$) get the same color. These two problems were proposed in the study of scalability of optical networks. In this paper, we provide upper and lower bounds on $χ'_d(n,q)$ and $χ_d(n,q)$ when $q$ is a prime power.

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Z. Han, M. Lu. 2015-10-28. On two $q$-ary $n$-cube coloring problems. https://arxiv.org/abs/1510.08168

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