Fang's multipartite cycle conjecture

Let $r\ge 3$ and let $n_{1}\ge n_{2}\ge \cdots\ge n_{r}\ge 1$. Let $K_{n_{1},n_{2},\ldots,n_{r}}$ be the complete $r$-partite graph with parts of these sizes, let $G$ be a subgraph of it, and let $f(n_{1},n_{2},\ldots,n_{r})$ be the edge threshold defined by Fang, Győri, Li and Xiao. A multipartite cycle is a cycle in which no two consecutive vertices lie in the same part. Fang's multipartite cycle conjecture. If

$$e(G)\ge f(n_{1},n_{2},\ldots,n_{r})+1,$$

then $G$ contains a multipartite cycle of length at most $\frac{3}{2}r$. The conjecture proposes a general threshold for forcing short multipartite cycles in complete multipartite graphs; the supplied text does not state whether it has been resolved.