  In this paper, we prove the following conjecture proposed by Gould, Hirohata
and Keller [Discrete Math. submitted]: Let $G$ be a graph of sufficiently large
order. If $\sigma_t(G) \geq 2kt - t + 1$ for any two integers $k \geq 2$ and $t
\geq 5$, then $G$ contains $k$ disjoint cycles.
