3 problems

Let $G(n,p)$ be the binomial random graph, and let the local resilience of a graph $G$ with respect to Hamiltonicity be the largest integer $r$ such that, for every subgraph…

Let ${\mathcal C}_{\mathcal H}^q$ denote the property that Client wins the $(1:q)$ Client-Waiter Hamiltonicity game on the random graph ${\mathcal G}(n,p)$, and let $p$ be the edge…

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…