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Questions tagged [hypercube]

For questions involving cubes in higher dimensions or the hypercube graphs.

14
votes
0answers
367 views

Monotone embedding of complete binary tree in hypercube

Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...
12
votes
4answers
718 views

Longest path through hypercube corners

Is the longest Hamiltonian path through the $2^d$ unit hypercube vertices known, where path length is measured by Euclidean distance in $\mathbb{R}^d$? The unit hypercube spans from $(0,0,\ldots,0)$ ...
5
votes
0answers
195 views

Longest simple path through hypercube corners

This is a variation on a previously answered question, Longest path through hypercube corners. Here I am seeking the longest simple (non-self-intersecting) path through the unit hypercube's vertices, ...
3
votes
1answer
121 views

Distance relation among points in high-dimensional hypercubes

Let $Q_{4n-1}$ be a unit hypercube of dimension $4n-1$. Has the following statement been proven? There are $4n$ vertices in $Q_{4n-1}$ such that the distance between each pair of them is $2\sqrt{...