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 …

A class of graphs $\mathscr {C} $ is monadically stable if for any unary expansion $\widehat
{\mathscr {C}} $ of $\mathscr {C} $, one cannot interpret, in first-order logic, arbitrarily long …

We introduce a novel model-theoretic framework inspired from graph modification and
based on the interplay between model theory and algorithmic graph minors. The core of our …

The disjoint paths logic, FOL+ DP, is an extension of First-Order Logic (FOL) with the extra
atomic predicate dp k (x 1, y 1,…, xk, yk), expressing the existence of internally vertex …

Given a graph $ G $ and a vertex set $ X $, the annotated treewidth tw $(G, X) $ of $ X $ in $
G $ is the maximum treewidth of an $ X $-rooted minor of $ G $, ie, a minor $ H $ where the …

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 …

An indiscernible sequence $(\bar a_i) _ {1\leq i\leq n} $ in a structure is an ordered
sequence of tuples of elements which is very homogeneous in the sense that any two finite …

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 …