Monadically dependent classes and efficient model checking

Establish whether efficient first-order model checking is obtainable on every monadically dependent graph class, as conjectured.

Background

The paper describes monadically dependent graph classes as classes from which the class of all graphs cannot be obtained by first-order transductions. It identifies efficient first-order model checking on such classes as a central conjectural objective in the area.

The conjecture is presented as motivation for studying which graph classes can and cannot be obtained from others by first-order transductions. It is not resolved by the paper, whose main result instead establishes a non-transducibility theorem for three-dimensional grids and bounded-genus graph classes.