Optimal cycles enclosing all the nodes of a -dimensional hypercube
R Rinaldi, M Rip��- arXiv preprint arXiv:2212.11216, 2022 - arxiv.org
R Rinaldi, M Rip�
arXiv preprint arXiv:2212.11216, 2022•arxiv.orgWe solve the general problem of visiting all the $2^ k $ nodes of a $ k $-dimensional
hypercube by using a polygonal chain that has minimum link-length, and we show that this
optimal value is given by $ h (2, k):= 3\cdot 2^{k-2} $ if and only if $ k\in\mathbb {N}-\{0, 1\} $.
Furthermore, for any $ k $ above one, we constructively prove that it is possible to visit once
and only once all the aforementioned nodes, $ H (2, k):=\{\{0, 1\}\times\{0,
1\}\times\dots\times\{0, 1\}\}\subset\mathbb {R}^ k $, with a cycle (ie, a closed path) having�…
hypercube by using a polygonal chain that has minimum link-length, and we show that this
optimal value is given by $ h (2, k):= 3\cdot 2^{k-2} $ if and only if $ k\in\mathbb {N}-\{0, 1\} $.
Furthermore, for any $ k $ above one, we constructively prove that it is possible to visit once
and only once all the aforementioned nodes, $ H (2, k):=\{\{0, 1\}\times\{0,
1\}\times\dots\times\{0, 1\}\}\subset\mathbb {R}^ k $, with a cycle (ie, a closed path) having�…
We solve the general problem of visiting all the nodes of a -dimensional hypercube by using a polygonal chain that has minimum link-length, and we show that this optimal value is given by if and only if . Furthermore, for any above one, we constructively prove that it is possible to visit once and only once all the aforementioned nodes, $H(2,k):=\{\{0,1\} \times \{0,1\} \times \dots \times \{0,1\}\} \subset \mathbb{R}^k$, with a cycle (i.e., a closed path) having only links.
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