Limits of Structures and the Example of Tree-Semilattices

Abstract : The notion of left convergent sequences of graphs introduced by Lov\' asz et al. (in relation with homomorphism densities for fixed patterns and Szemer\'edi's regularity lemma) got increasingly studied over the past $10$ years. Recently, Ne\v set\v ril and Ossona de Mendez introduced a general framework for convergence of sequences of structures. In particular, the authors introduced the notion of $QF$-convergence, which is a natural generalization of left-convergence. In this paper, we initiate study of $QF$-convergence for structures with functional symbols by focusing on the particular case of tree semi-lattices. We fully characterize the limit objects and give an application to the study of left convergence of $m$-partite cographs, a generalization of cographs.
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https://hal.archives-ouvertes.fr/hal-01150659
Contributor : Patrice Ossona de Mendez <>
Submitted on : Thursday, September 17, 2015 - 8:22:20 AM
Last modification on : Wednesday, November 6, 2019 - 10:50:21 AM
Long-term archiving on : Wednesday, April 26, 2017 - 6:39:20 PM

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  • HAL Id : hal-01150659, version 2
  • ARXIV : 1505.03037

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Pierre Charbit, Lucas Hosseini, Patrice Ossona de Mendez. Limits of Structures and the Example of Tree-Semilattices. 2015. ⟨hal-01150659v2⟩

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