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We prove that if $G$ is connected, then $\\iota(G,k) \\leq \\frac{n}{k+1}$ unless $G$ is a $k$-clique or $k = 2$ and $G$ is a $5$-cycle. The bound is sharp. The case $k=1$ is a classical result of Ore, and the case $k=2$ is a recent result of Caro and Hansberg. 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