More efficient constructions of finite common coverings

Determine whether finite common coverings of the regular generalized graphs used to construct graphs with independent exact r-covers can be constructed more efficiently than the covering constructions currently employed.

Background

The paper constructs graphs with independent exact r-covers by taking common coverings of smaller regular generalized graphs. The resulting upper bound for N(d) is the product of d+1 through 2d, while the lower bound is substantially smaller. The authors note that closing this super-exponential gap may require new ideas and explicitly leave unresolved whether more efficient common-covering constructions exist.