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Consider the vertices of an $n$-dimensional cube. The distance between two vertices is measured as the minimum number of edges between the two vertices. Now consider a subset of these vertices. If we ...

Let $G$ be a plane $3$-connected graph; so it partitions the plane into regions bounded by faces. Let $\mathrm{deg}_v$ be the sequence of vertex degrees of $G$, and $\mathrm{deg}_f$ be the sequence of ...

The question is inspired by this previous MO question. There it was shown that it's possible to label the edges of a cube by the numbers $\{1,2,\ldots,6,8,9, \ldots, 13\}$ in such a way that: Three ...

While there exist regular tesselations of the hyperbolic plane with arbitrary regular polygons, there are no new regular polyhedra in hyperbolic (3D) space. This being quite trivial, it is probably ...