2 problems

Uniform connected subgraph p-NC conjecture. For every $n$ for which the measure is defined, $\mathbb{P}_{\mathrm{UC}}$ satisfies the p-NC property.

Let $K_\NN$ be the complete graph on the positive integers. For a subgraph $T$ of $K_\NN$, write $\bar d(T)$ for the upper density of its vertex set and $\bar d_S(T)$ for its stron…