Abstract
For an integer t, where \(t \geqslant 2\), let \(\sigma _t(G)\) denote the minimum degree sum of an independent set with t vertices in a graph G. We prove that for two integers k, t with \(k \geqslant 3\), \(t \geqslant 4\), every graph G with \(|V(G)| \geqslant kt+1.5k+t\) and \(\sigma _t(G) \geqslant 2kt - t + 1\) contains k disjoint cycles. This result improves the theorem of Ma and Yan by optimizing the lower bound of |V(G)|. In addition, we also improve the theorem of Gould et al. for \(t =4\) and \(k \geqslant 2\).
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C.-J. Song contributed to the theoretical derivation and wrote the manuscript. Y. Wang contributed to the solutions to difficult problems and revised the manuscript. J. Yan contributed to the conception of the study and revised the manuscript.
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This research was supported by the National Natural Science Foundation of China (No. 12071260).
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Song, CJ., Wang, Y. & Yan, J. Disjoint Cycles and Degree Sum Condition in a Graph. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00473-5
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DOI: https://doi.org/10.1007/s40305-023-00473-5