The confirmation of a conjecture on disjoint cycles in a graph

Let $t$ and $k$ be two integers with $t\ge 5$ and $k\ge 2$. For a graph $G$ and a vertex $x$ of $G$, we use $d_G\left(x\right)$ to denote the degree of $x$ in $G$. Define ${\sigma }_t\left(G\right)$ to be the minimum value of ${\sum }_{x\in X}{d}_G\left(x\right)$, where $X$ is an independent set of $G$ with $\left|X\right|=t$. This paper proves the following conjecture proposed by Gould et al. (2018). If $G$ is a graph of sufficiently large order with ${\sigma }_t\left(G\right)\ge 2kt?t+1$, then $G$ contains $k$ vertex-disjoint cycles.