Gould–Hirohata–Keller conjecture on degree sums for disjoint cycles

Let $G$ be a graph of sufficiently large order. For an integer $t\geq 1$, let $\sigma_t(G)$ denote the minimum degree sum over all sets of $t$ pairwise nonadjacent vertices of $G$. Gould–Hirohata–Keller conjecture. If $\sigma_t(G)\geq 2kt-t+1$ for any two integers $k\geq 2$ and $t\geq 4$, then $G$ contains $k$ disjoint cycles. This conjecture proposes a general degree-sum condition extending known sharp results for disjoint cycles; its resolution would clarify how degree sums over independent vertex sets guarantee collections of vertex-disjoint cycles.