  The generalized Kneser graph $K(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is
the graph whose vertices are the $k$-subsets of $\{1,\dots,n\}$ with two
vertices adjacent if and only if they share less than $t$ elements. We
determine the treewidth of the generalized Kneser graphs $K(n,k,t)$ when $t\ge
2$ and $n$ is sufficiently large compared to $k$. The imposed bound on $n$ is a
significant improvement of a previously known bound. One consequence of our
result is the following. For each integer $c\ge 1$ there exists a constant
$K(c)\ge 2c$ such that $k\ge K(c)$ implies for $t=k-c$ that
$$tw(K(n,k,t))=\binom{n}{k}-\binom{n-t}{k-t}-1$$ if and only if $n\ge
(t+1)(k+1-t)$ .
