  An axis-parallel $d$-dimensional box is a cartesian product $I_1\times
I_2\times \dots \times I_b$ where $I_i$ is a closed sub-interval of the real
line. For a graph $G = (V,E)$, the $boxicity \ of \ G$, denoted by
$\text{box}(G)$, is the minimum dimension $d$ such that $G$ is the intersection
graph of a family $(B_v)_{v\in V}$ of $d$-dimensional boxes in $\mathbb R^d$.
Let $k$ and $n$ be two positive integers such that $n\geq 2k+1$. The $Kneser \
graph$ $Kn(k,n)$ is the graph with vertex set given by all subsets of
$\{1,2,\dots,n\}$ of size $k$ where two vertices are adjacent if their
corresponding $k$-sets are disjoint.
  In this note, we derive a general upper bound for $\text{box}(Kn(k,n))$, and
a lower bound in the case $n\ge 2k^3-2k^2+1$, which matches the upper bound up
to an additive factor of $\Theta(k^2)$. Our second contribution is to provide
upper and lower bounds for the boxicity of the complement of the line graph of
any graph $G$, and as a corollary, we derive that $\text{box}(Kn(2,n))\in
\{n-3, n-2\}$ for every $n\ge 5$.
