Related papers: Characterizations of monadically dependent tree-or…
We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…
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 monadically dependent. Originating in model theory,…
Tree-ordered weakly sparse models have recently emerged as a robust framework for representing structures in an ``almost sparse'' way, while allowing the structure to be reconstructed through a simple first-order interpretation. A prominent…
It is known that for subgraph-closed graph classes the first-order model checking problem is fixed-parameter tractable if and only if the class is nowhere dense [Grohe, Kreutzer, Siebertz, STOC 2014]. However, the dependency on the formula…
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 generalize nowhere dense classes and constitute important examples…
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths -- a result that shows a strong link between the properties of these graph classes considered from the…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
Connections between structural graph theory and finite model theory recently gained a lot of attention. In this setting, many interesting questions remain on the properties of dependent (NIP) hereditary classes of graphs, in particular…
We study the model-checking problem for first- and monadic second-order logic on finite relational structures. The problem of verifying whether a formula of these logics is true on a given structure is considered intractable in general, but…
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 that the model checking problem for first-order logic is…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
Stability and dependence are model-theoretic notions that have recently proved highly effective in the study of structural and algorithmic properties of hereditary graph classes, and are considered key notions for generalizing to hereditary…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
We prove several negative results about first-order transducibility for classes of sparse graphs: - for every $t \in \mathbb{N}$, the class of graphs of treewidth at most $t+1$ is not transducible from the class of graphs of treewidth at…
We give new decomposition theorems for classes of graphs that can be transduced in first-order logic from classes of sparse graphs -- more precisely, from classes of bounded expansion and from nowhere dense classes. In both cases, the…
We prove that for any monotone class of finite relational structures, the first-order theory of the class is NIP in the sense of stability theory if, and only if, the collection of Gaifman graphs of structures in this class is nowhere…
Treewidth is an important graph invariant, relevant for both structural and algorithmic reasons. A necessary condition for a graph class to have bounded treewidth is the absence of large cliques. We study graph classes closed under taking…
Classes with bounded rankwidth are MSO-transductions of trees and classes with bounded linear rankwidth are MSO-transductions of paths. These results show a strong link between the properties of these graph classes considered from the point…
Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…