Questions tagged [hypercube]
For questions involving cubes in higher dimensions or the hypercube graphs.
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Number of hypercube unfoldings
While writing the code for this answer, I noticed that I not only could calculate the number of unfoldings of the $4$-cube, but also the number of the $n$-cube for more values of $n$. Basically, we ...
24
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answer
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Which unfoldings of the $d$-dimensional hypercube tile $(d{-}1)$-space?
A six year old question,
Which unfoldings of the hypercube tile $3$-space?, has just been answered by
Moritz Firsching:
All $261$ unfoldings tile space!
So now we know:
For $d=2$, the unfolding of ...
14
votes
0
answers
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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
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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
0
answers
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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
1
answer
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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{...