The confirmation of a conjecture on disjoint cycles in a graph

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.