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Let $n$, $k$ and $t$ be integers with $1\leq t< k \leq n$. The\emph{generalized Kneser graph} $K(n,k,t)$ is a graph whose vertices are the$k$-subsets of a fixed $n$-set, where two $k$-subsets $A$ and $B$ are adjacentif $|A\cap B|<t$. The graph $K(n,k,1)$ is the well-known \emph{Kneser graph}.In 2014, Harvey and Wood determined the exact treewidth of the Kneser graphsfor large $n$ with respect to $k$. In this paper, we give the exact treewidthof the generalized Kneser graphs for $t\geq2$ and large $n$ with respect to $k$and $t$. In the special case when $t=k-1$, the graph $K(n,k,k-1)$ usuallydenoted by $\overline{J(n,k)}$ which is the complement of the Johnson graph$J(n,k)$. We give a more precise result for the exact value of the treewidth of$\overline{J(n,k)}$ for any $n$ and $k$.

Treewidth of the generalized Kneser graphs