Davoodi–Javadi–Omoomi lower-bound conjecture for sigma clique coverings

Let $K_t(d)$ be the complete $t$-partite graph with each part of size $d$. Davoodi–Javadi–Omoomi's conjecture. There exists a function $f$ and a constant $c>0$ such that, for every positive integers $t$ and $d$, if $t\geq f(d)$, then

$$\operatorname{scc}(K_t(d))\geq cd^2t\log t.$$

This conjecture predicts that complete multipartite graphs attain, up to a constant factor, the logarithmic upper bound for the sigma clique cover number when the number of parts is sufficiently large relative to their size. The paper presents an equivalent set-system formulation and proves related lower bounds, but the stated asymptotic bound remains open.