2 problems

Far-from-Turán eigenvalue conjecture. For every $\varepsilon>0$, there exists $c>0$ such that, if $G$ is a regular $n$-vertex graph that is $\varepsilon$-far from every Turán graph…

Let $g_3(n,e)$ be the minimum number of triangles in an $(n,e)$-graph. Let $\mathcal{H}_0^*(n,e)$ and $\mathcal{H}_2^*(n,e)$ denote the subclasses of $\mathcal{H}_0(n,e)$ and…