3 problems

Local resilience conjecture. For every $\epsilon\in (0,1/2]$ and integer $d\geq1$, there exists a constant $C=C(d,\epsilon)>0$ such that, for $r\geq C(\log n/n)^{1/d}$, asymptotica…

Shifted Chvátal-resilience conjecture. For every $\varepsilon>0$, there exists $C>0$ such that, for $p\geq C\log n/n$, a.a.s. the random graph $G_{n,p}$ is…

Let $\mathcal{G}(n,p)$ be the binomial random graph on $n$ vertices, let $\mathcal{HAM}$ denote the property of being Hamiltonian, and let $r_\ell(G,\mathcal{HAM})$ denote the loca…