Disjoint cycles in graphs with restricted independence number (Q2166216)

\textit{H. A. Kierstead} et al. [J. Comb. Theory, Ser. B 122, 121--148 (2017; Zbl 1350.05072)] showed that, for \(k\geq 3\), every graph with \(n\geq 3k\) vertices, minimum degree at least \(2k-1\) and independence number at most \(n-2k-1\) has \(k\) vertex-disjoint cycles. In this paper, the authors extend the above result by showing that there exist \(\beta>0\) and \(t_0\) such that for every \(t\geq t_0\), \(k\geq 25t\) and \(n\geq 4k+t\), every graph on \(n\) vertices with minimum degree at least \(2k-t\) and independence number at most \(n-2k-t+\beta\sqrt{t\log t}\) contains \(k\) vertex-disjoint cycles.