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3 questions
1
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0
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Do cycle graphs embed isometrically in spheres?
I recently came across, what seems to be a folklore. Namely, that cycle graphs embeds isometrically into spheres $S^n(r)$, for some $n\in \mathbb{N}_+$ and some $r>0$. However, I could not track ...
4
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3
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430
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How to show that random graphs cannot be embedded with short edges
For each (not necessarily planar) embedding of a graph in $\mathbb{R}^k$ one can calculate the ratio
$$\gamma = \frac{\textsf{mean Euclidean length of edges}}{\textsf{mean Euclidean distance between ...
4
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1
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700
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Embedding graphs into hyperbolic spaces
Do we know of a characterization as to when does a graph have a "good" embedding into a hyperbolic space? (And does having such an embedding have a spectral or wavelet analysis signature?)
I don't ...