A Unified Approach to Structural Limits and Limits of Graphs With Bounded Tree-Depth - Brossura

Nesetril, Jaroslav; De Mendez, Patrice Ossona

 
9781470440657: A Unified Approach to Structural Limits and Limits of Graphs With Bounded Tree-Depth

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Nesetril and de Mendez introduce a general framework for the study of limits of relational structures-graphs in particular-that is based on a combination of model theory and functional analysis. They show how the various approaches to graph limits fit this framework, and that they naturally appears as "tractable cases" of a general theory. As an outcome of this, they provide extensions of known results that they believe situates them in a broader context. In the second part of the paper, they study sparse structures, considering limits of structures with components that are connected by a bounded diameter, and proving that in this case, the convergence can be "almost" studied component-wise. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)

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