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The path covering number, $\\rm{pc}(G)$, of $G$ is the minimum number of vertex disjoint paths such that every vertex belongs to a path in the cover. We show that if $G$ has order $n$, then $\\alpha'(G) + \\frac{1}{2}\\rm{pc}(G) \\ge \\frac{n}{2}$ and we provide a constructive characterization of the graphs achieving equality in this bound. 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