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For questions involving cubes in higher dimensions or the hypercube graphs.
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Inequality involving size of nodes & min degree of graph
$G$ above corresponds to an $n$-dimensional hypercube, so $G'=(V',E')$ is necessarily a subgraph of the hypercube. Let $v$ be any vertex in $V'$ (and hence also in $V$). … A trivial example to show this bound is tight is to take a hypercube of dimension $d$ on the boundary of the original hypercube, as this has exactly $2^d$ vertices and has degree $d$ for all vertices. …