4 problems

Let $G_{n,p,d}$ denote the class of $d$-dependent random graph distributions on graphs with $n$ vertices and marginal edge probability $p$. Let $\mathcal{P}$ be a monotone graph pr…

Let $G_{n,p,d}$ denote the class of $d$-dependent random graph distributions on graphs with $n$ vertices and marginal edge probability $p$. Let $d4ab$ be a monotone graph property,…

Forest boundary conjecture. For any tree $T$, the class of $\{T,\overline{T^b}\}$-free bipartite graphs is at most factorial.

Let a graph or digraph property be monotone if it is preserved under deletion of edges or arcs, and let a property be non-trivial if it is neither always true nor always false. A p…