On the treewidth of generalized q-Kneser graphs

The generalized q-Kneser graph Kq(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 Fq-vectorspace with two vertices U₁ and U₂ adjacent if and only if (U₁∩ U₂)<t. We determine the treewidth of the generalized q-Kneser graphs Kq(n,k,t) when t≥ 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 Kq(n,k,t) with $k>t>0$ and n≥ 3k-t+9 is equal to nk-n-tk-t-1.