Kostochka–Mubayi–Verstraëte loose 5-cycle Ramsey conjecture

For each $k\geq3$, let $LC_5^{(k)}$ be the $k$-uniform loose 5-cycle, and let $r_k(LC_5,n)$ denote its Ramsey number against a complete $k$-uniform hypergraph on $n$ vertices. Kostochka–Mubayi–Verstraëte conjecture. There is a constant $c=c_k>0$ such that

$$r_k(LC_5,n)<c n^{5/4}.$$

The source records a lower bound of order $(n/\log n)^{5/4}$ and presents this as the conjectured matching polynomial upper bound. The correct order remains open.