3 problems

Let $d_0,c>0$ be universal constants. For every integer $d\geq d_0$, let $G$ be a connected $n$-vertex graph with minimum degree at least $d$, and let $\mathcal{T}$ be a uniformly…

Fix an integer $\delta\geq 1$ and a graph $H$. Let $\mathcal{G}(n,\delta)$ be the family of all $n$-vertex graphs with minimum degree $\delta$, and let $c(\delta,H)$ be a constant…

Let $n$ and $\beta$ be such that the family of graphs $\mathcal{G}(n,\beta)$ is defined, and let $(n,\beta)$ be feasible when $G[V_0]$ is triangle-free for…