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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