Reconstruction conjecture for quasi Cartesian products

A quasi Cartesian product is a graph with the local product-like structure described above. Reconstruction conjecture. Quasi Cartesian products can be reconstructed in essentially the same time from vertex-deleted subgraphs as Cartesian products. This predicts that the efficient reconstruction methods available for Cartesian products extend, up to essentially the same running time, to quasi Cartesian products; the source provides no resolution of the conjecture.