Efficient first-order model checking for monadically dependent graph classes

Establish whether monadic dependence is sufficient to obtain an efficient first-order model-checking algorithm for a graph class; equivalently, determine whether every monadically dependent graph class admits efficient first-order model checking.

Background

The paper discusses monadically dependent graph classes, defined as graph classes from which the class of all graphs cannot be first-order transduced. It notes a conjecture that monadic dependence captures precisely the graph classes on which efficient first-order model checking can be obtained. This conjecture is cited as broader motivation for studying first-order transduction non-transducibility, but it is not resolved in the paper.