Subspace intersection graphs

Given a set RR of affine subspaces in RdRd of dimension ee, its intersection graph GG has a vertex for each subspace, and two vertices are adjacent in GG if and only if their corresponding subspaces intersect. For each pair of positive integers dd and ee we obtain the class of (d,e)(d,e)-subspace intersection graphs. We classify the classes of (d,e)(d,e)-subspace intersection graphs by containment, for e=1e=1 or e=d−1e=d−1 or d≤4d≤4.