  For every graph $G$, let $\alpha(G)$ denote its independence number. What is
the minimum of the maximum degree of an induced subgraph of $G$ with
$\alpha(G)+1$ vertices? We study this question for the $n$-dimensional Hamming
graph over an alphabet of size $k$. In this paper, we give a construction to
prove that the answer is $1$ for all $n$ and $k$ with $k \geq 3$. This is an
improvement over an earlier work showing that the answer is at most $\lceil
\sqrt{n} \, \rceil$.
