Gray-code path embedding of a grid in a hypercube
= Gray-code path embedding of a grid in a hypercube
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The order $00,01,11,10$ is a <Gray code> through the four vertices of $Q_2$. Applying this identification independently in $n$ coordinate pairs makes $[4]^n=P_4^n$ a <spanning subgraph> of the <hypercube graph> $Q_{2n}$. Therefore every vertex boundary in $Q_{2n}$ contains the corresponding boundary in $[4]^n$.