3 problems

Let $\bar d(G)$ denote the upper density of the vertex set of a graph $G$ embedded in $K_\NN$. Bounded-degree density conjecture. For every $\Delta\in\NN$, there exists $c>0$ such…

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…

Let $K_\NN$ be the complete graph on the positive integers, and define the upper density of a vertex set $A\subseteq\NN$ by $\bar d(A)=\limsup_{n\to\infty}|A\cap[n]|/n$. The upper…