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 graph class $\mathscr {C} $ is called monadically stable if one cannot interpret, in first-
order logic, arbitrary large linear orders in colored graphs from $\mathscr {C} $. We prove …

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 …

Disjoint-paths logic, denoted FO+ DP, extends first-order logic (FO) with atomic predicates
dp k [(x 1, y 1),…,(xk, yk)], expressing the existence of internally vertex-disjoint paths …

The dynamics of real-world applications and systems require efficient methods for improving
infeasible solutions or restoring corrupted ones by making modifications to the current state …

We consider the flip-width of geometric graphs, a notion of graph width recently introduced
by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip …

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 …

A $ k $-subcolouring of a graph $ G $ is a function $ f: V (G)\to\{0,\ldots, k-1\} $ such that the
set of vertices coloured $ i $ induce a disjoint union of cliques. The subchromatic number …

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 …