# On the central levels problem

@article{Gregor2020OnTC, title={On the central levels problem}, author={Petr Gregor and Ondrej Micka and Torsten M{\"u}tze}, journal={ArXiv}, year={2020}, volume={abs/1912.01566} }

The central levels problem asserts that the subgraph of the $(2m+1)$-dimensional hypercube induced by all bitstrings with at least $m+1-\ell$ many 1s and at most $m+\ell$ many 1s, i.e., the vertices in the middle $2\ell$ levels, has a Hamilton cycle for any $m\geq 1$ and $1\le \ell\le m+1$. This problem was raised independently by Savage, by Gregor and Skrekovski, and by Shen and Williams, and it is a common generalization of the well-known middle levels problem, namely the case $\ell=1$, and…

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