A Kneser hypergraph is a hypergraph with the vertices being the subsets of $M=\{1,2,\dots,m\}$ of size $l$ and the edges being the collections of size $r$ of these subsets such that any two subsets are disjoint. The Alon-Frankl-Lovasz theorem gives the chromatic number of this graph.
Has a variant of this been considered, where instead of any two subsets of the collection having to be disjoint (or equivalently, any element $i\in M$ appears in at most one subset of the collection), we require that any element $i\in M$ appears in at most $d$ subsets of the collection for some value $d>1$? If so, is there a corresponding result on the chromatic number?
