The generalized q-Kneser graph \(K_q(n,k,t)\) for integers \(k>t>0\) and \(n>2k-t\) is the graph whose vertices are the k-dimensional subspaces of an n-dimensional \(F_q\) -vector space with two vertices \(U_1\) and \(U_2\) adjacent if and only if \(\dim (U_1\cap U_2)<t\) . We determine the treewidth of the generalized q-Kneser graphs \(K_q(n,k,t)\) when \(t\ge 2\) and n is sufficiently large compared to k. The imposed bound on n is a significant improvement of the previously known bound. One consequence of our results is that the treewidth of each q-Kneser graph \(K_q(n,k,t)\) with \(k>t>0\) and \(n\ge 3k-t+9\) is equal to \({n\brack k}_q-{n-t\brack k-t}_q-1.\)
