All Questions

Harborth's conjecture states that every planar graph can be drawn on a plane only using staight line segments of rational or integral edge length. ( There is a good mathoverflow page for this ...

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 ...

I'm trying to find the number of distinguishable knot projections over certain convex regular polyhedra according to the following constraints. On each face on the polyhedron the knot will have a ...

Consider Associahedron, consider graph build from its vertices and edges. Choose some vertex. Let us count the number of vertices on distances $k$ from the selected vertex. Write a generating ...

Suppose $F$ is a face of a 2-complex, and $F_1,\dotsc,F_n$ are the faces that are adjacent to (i.e., share an edge with) $F$. Is there a standard term for a collection of faces of the form $\{F,F_1,\...