Treewidth of the q-Kneser graphs

Let V be an n-dimensional vector space over a finite field F-q, where q is a prime power. Define the generalized q-Kneser graph K-q(n, k, t) to be the graph whose vertices are the k-dimensional subspaces of V and two vertices F-1 and F-2 are adjacent if dim(F-1 boolean AND F-2) < t. Then K-q(n, k, 1) is the well-known q-Kneser graph. In this paper, we determine the treewidth of K-q(n, k, t) for n >= 2t(k - t + 1) + k + 1 and t >= 1 exactly. Especially, for any possible n, k and q we also determine the treewidth of K-q(n, k, k - 1), which is the complement of the Grassmann graph G(q)(n, k).