3 problems

Let $C_n^k$ denote the $k$th power of the cycle on $n$ vertices, and let $\varepsilon>0$. The random sub-sampling local-resilience conjecture. There exists $k$ large enough such th…

Let $n$ and $k$ be positive integers. Consider the Cayley graph on $4\mathds{Z}/n\mathds{Z}4$ with generating set $\{-k,\ldots,k\}\setminus\{0\}$. Espuny Díaz, Lichev, and Wesolek'…

Let $C_n$ be a cycle on $n$ vertices, and let $C_n^d$ be its $d$th power: two distinct vertices are adjacent when their distance in $C_n$ is at most $d$. The rna number $c3^{-}(G)$…