2 problems

Let $KG(n,k)_{s-\mathrm{stab}}$ be the induced subgraph of the Kneser graph $KG(n,k)$ on the $s$-stable $k$-subsets of $[n]$, where a subset $A$ is $s$-stable when…

For positive integers $n,k,r$ with $k\geq 2$, $r\geq 2$, and $n\geq rk$, let $KG^{r}(n,k)_{r\text{-}stab}$ be the $r$-stable $r$-uniform Kneser hypergraph, and let $KG^{r}(n,k)$ be…