Polynomial-time solvability for cores of bounded-$\lambda$ structure classes

Establish whether a recursively enumerable class of finite relational structures whose parameter $\lambda$ is bounded has polynomial-time solvable homomorphism problems whenever the cores of its structures have bounded fractional hypertree width.

Background

For classes of structures with bounded incidence degeneracy, the paper proves that bounded fractional hypertree width of the cores implies polynomial-time solvability of the homomorphism problem. The authors identify the extension from bounded incidence degeneracy to bounded $\lambda$ as an unresolved gap, because the available algorithmic transfer relies on bounded VC dimension.