The confirmation of a conjecture on disjoint cycles in a graph

Let t and k be two integers with t≥5 and k≥2. For a graph G and a vertex x of G, we use dG(x) to denote the degree of x in G. Define σt(G) to be the minimum value of ∑x∈XdG(x), where X is an independent set of G with |X|=t. This paper proves the following conjecture proposed by Gould et al. (2018). If G is a graph of sufficiently large order with σt(G)≥2kt−t+1, then G contains k vertex-disjoint cycles.