7 problems

Conlon–Lee's conjecture. If $G$ is a bigraph that is edge-transitive under the action of $\operatorname{FoldGroup}(G)$, then $G$ is cut-percolating.

Let ${\bf d}=(d_1,\ldots,d_n)$ be a degree sequence and let $M_i=\sum_{j=1}^n(d_j)_i$ with $(x)_i=\prod_{j=0}^{i-1}(x-j)$. Let $M_1$ and $M_2$ be the first two falling-factorial de…

Let ${\bf d}=(d_1,\ldots,d_n)$ be a degree sequence, let $M_i=\sum_{j=1}^n(d_j)_i$ with $(x)_i=\prod_{j=0}^{i-1}(x-j)$, and let $n_1$ and $n_2$ denote the numbers of vertices of de…

Let $G$ be a large but finite graph with negative curvature. Suppose its symmetric group fixes a unique point $v_0$. Let the inertia and demand of a vertex be the quantities define…

Let $G$ be a large but finite graph with positive curvature. A graph is vertex-transitive when for every pair of vertices there is a graph isomorphism taking one to the other. Let…

Finiteness conjecture. There are finitely many finite, primitive amalgams of degree $(p,q)$ where $p$ and $q$ are primes.

Tetrahedral embedding conjecture. Each graph $G\in{\cal P}$ with one point orbit can be embedded on the sphere of the solid regular tetrahedron in such a way that all four induced…