Related papers: First-order limits, an analytical perspective
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…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
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…
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…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
We introduce and develop a theory of limits for sequences of sparse graphs based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs…
Ne\v{s}et\v{r}il and Ossona de Mendez recently proposed a new definition of graph convergence called structural convergence. The structural convergence framework is based on the probability of satisfaction of logical formulas from a fixed…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
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…
In recent years there has been much progress in graph theory on questions of the following type. What is the threshold for a certain large substructure to appear in a random graph? When does a random graph contain all structures from a…
We present a new approach to graph limit theory which unifies and generalizes the two most well developed directions, namely dense graph limits (even the more general $L^p$ limits) and Benjamini--Schramm limits (even in the stronger…
A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that the collection of finite structures can be embedded, via a map they call the Stone pairing, in a…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.