All Questions

The face lattice of a convex polytope $P\subset\Bbb R^d$ is the partially ordered set whose elements are the faces of $P$ ordered by inclusion. We can turn it into a graph by considering its Hasse ...

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 ...

I want to find a map $v\mapsto \tilde v$ from the vertex set of a connected infinite graph $\Gamma$ to a Euclidean space that meets the following two conditions: there is $\varepsilon>0$ such that ...

There is a folklore in the empirical computer-science literature that, given a tree $(X,d)$, one can find a bi-Lipschitz embedding into a hyperbolic space $\mathbb{H}^n$ and that $n$ is "much ...

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 ...

Consider a graph $G$ with nonnegative edge weights. Question: In $\mathbb{R}^3$, how hard is it to assign coordinates to vertices such that the Euclidean length of each edge is equal to its weight? ...