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A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth by Patrice Ossona de Mendez, Jaroslav Nesetril (Paperback, 2020)

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In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as tractable cases'' of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be almost'' studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as elementary bricks'' these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first ``intermediate class'' with explicitly defined limit structures where the inverse problem has been solved.

Product Identifiers

PublisherAmerican Mathematical Society

ISBN-139781470440657

eBay Product ID (ePID)14046449262

Product Key Features

SubjectMathematics

Publication Year2020

Number of Pages108 Pages

Publication NameA Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth

LanguageEnglish

TypeTextbook

AuthorPatrice Ossona De Mendez, Jaroslav Nesetril

FormatPaperback

Dimensions

Item Height254 mm

Item Width178 mm

Additional Product Features

Country/Region of ManufactureUnited States

Title_AuthorPatrice Ossona De Mendez, Jaroslav Nesetril

Series TitleMemoirs of the American Mathematical Society