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Jaroslav Neˇsetˇril, Patrice Ossona de Mendez A model theory approach to structural limits

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Jaroslav Neˇ setˇ ril, Patrice Ossona de Mendez A model theory approach to structural limits

Comment.Math.Univ.Carolin. 53,4 (2012) 581 –603.

Abstract: 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 example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.

Keywords: graph, graph limits, model theory, first-order logic AMS Subject Classification: 05C99

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[21] Neˇsetˇril J., Ossona de Mendez P.,Sparsity. Graphs, Structures, and Algorithms, Algorithms and Combinatorics, 28, Springer, Heidelberg, 2012, 465 pp.

[22] Neˇsetˇril J., Ossona de Mendez P.,Graph limits: a unified approach with application to the study of limits of graphs with bounded diameter components, manuscript, 2012.

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