2 problems

For integers $k\ge 3$, let $f_1(e,q,k)$ denote the maximum chromatic number of a $1$-$(q,k)$-system with $e$ $q$-cliques. The asymptotic chromatic-number conjecture. Fix $k\ge 3$.…

Defective-colouring conjecture. Every $(r+1)$-uniform linear hypergraph with maximum degree at most $\Delta$ has a $d$-defective colouring with