Abstract
For a graph G, let n(G), \(\alpha (G)\) and \(\beta (G)\) be its order, independence number and matching number, respectively. We showed that \(\frac{\Delta (G)+k}{4}\alpha (G) + \beta (G) \ge n(G)\) for some \(K_k\)-free graph G with \(\Delta (G)\ge k-1\ge 2\).
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Acknowledgements
The authors are grateful to the referees for their invaluable comments, particularly comments for the proof of Theorem 1 (Theorem 2 in original manuscript), which improves the presentation of the manuscript greatly. One of referees pointed that the easy proof for Remark 1 (Theorem 1 in original manuscript).
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Supported in part by NSFC, NSF of Zhejiang, and a Grant of Jiaxing.
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Chen, M., Li, Y. & Yang, Y. Independence and matching number of some graphs. J Comb Optim 37, 1342–1350 (2019). https://doi.org/10.1007/s10878-018-0356-9
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DOI: https://doi.org/10.1007/s10878-018-0356-9