Subspace intersection graphs

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