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Monotone graph limits and quasimonotone graphs

Abstract:

The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a symmetric function $W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence ...

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Authors


Bollobas, B More by this author
Riordan, O More by this author
Journal:
Internet Mathematics 8 (2012), 187-231
Volume:
8
Issue:
3
Pages:
187-231
Publication date:
2011-01-22
DOI:
EISSN:
1944-9488
ISSN:
1542-7951
URN:
uuid:f403f1e7-390d-4d47-9812-aa7b57c66f22
Source identifiers:
146881
Local pid:
pubs:146881
Keywords:

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