New Bounds on a Hypercube Coloring Problem
1999-03-03
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New Bounds on a Hypercube Coloring Problem
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1999-03-03
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On studying the scalability of optical networks, one problem arising is to color the vertices of the $n$-cube with as few colors as possible such that any two vertices whose Hamming distance is at most $k$ are colored differently. Determining the exact value of $chi_k(n)$, the minimum number of colors needed, is a difficult problem.
In this paper, we improve the lower and upper bounds of $chi_k(n)$ and indicate the connection of this coloring problemto linear codes.
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Ngo, Hung Q.; Du, Ding-Zhu. (1999). New Bounds on a Hypercube Coloring Problem. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/215366.
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