Multigraph limits, unbounded kernels, and Banach space decorated graphs

We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional analytic framework provides a universal language for various combinatorial limit notions. In particular it makes it possibl...

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Bibliographic Details
Published in:Journal of functional analysis 2022-01, Vol.282 (2), p.109284, Article 109284
Main Authors: Kunszenti-Kovács, Dávid, Lovász, László, Szegedy, Balázs
Format: Article
Language:English
Subjects:
Banach spaces
Graph limits
Graphons
Kernel operators
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Summary:We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional analytic framework provides a universal language for various combinatorial limit notions. In particular it makes it possible to assign limit objects to multigraph sequences that are convergent in the sense of node-and-edge homomorphism numbers, and it generalizes the limit theory for graph sequences with compact decorations.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2021.109284