Related papers: First-order interpretations of bounded expansion c…
Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…
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…
Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
Nowhere dense graph classes, introduced by Nesetril and Ossona de Mendez, form a large variety of classes of "sparse graphs" including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and…
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an existential first-order formula. As a consequence, we derive, on bounded…
It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
Nesetril and Ossona de Mendez introduced the notion of first order convergence as an attempt to unify the notions of convergence for sparse and dense graphs. It is known that there exist first order convergent sequences of graphs with no…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence…
Classes with bounded expansion, which generalise classes that exclude a topological minor, have recently been introduced by Ne\v{s}et\v{r}il and Ossona de Mendez. These classes are defined by the fact that the maximum average degree of a…
We introduce an algorithm that constructs a random uniform graph with prescribed degree sequence together with a depth first exploration of it. In the so-called supercritical regime where the graph contains a giant component, we prove that…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
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,…
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…