A graph class C is called monadically stable if one cannot interpret, in first-order logic,
arbitrary large linear orders in colored graphs from C. We prove that the model checking …

A class of graphs is structurally nowhere dense if it can be constructed from a nowhere
dense class by a first-order transduction. Structurally nowhere dense classes vastly …

We define new graph parameters, called flip-width, that generalize treewidth, degeneracy,
and generalized coloring numbers for sparse graphs, and clique-width and twin-width for …

A conjecture in algorithmic model theory predicts that the model-checking problem for first-
order logic is fixed-parameter tractable on a hereditary graph class if and only if the class is …

Tractability results for the model checking problem of logics yield powerful algorithmic meta
theorems of the form: Every computational problem expressible in a logic $ L $ can be …

Low treedepth decompositions are central to the structural characterizations of bounded
expansion classes and nowhere dense classes, and the core of main algorithmic properties …

Monadically stable and monadically NIP classes of structures were initially studied in the
context of model theory and defined in logical terms. They have recently attracted attention …

A graph class is monadically stable if it does not encode the class of all linear orders using
first-order logic and vertex colors. This includes many sparse classes like planar graphs …

Graph transformations definable in logic can be described using the notion of transductions.
By understanding transductions as a basic embedding mechanism, which captures the …

We use model-theoretic tools originating from stability theory to derive a result we call the
Finitary Substitute Lemma, which intuitively says the following. Suppose we work in a stable …