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We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors).
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O. Kallenberg, Probabilistic Symmetries and Invariance Principles . Springer, New York, 2005
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C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós, B. Szegedy and K. Vesztergombi, Graph limits and parameter testing. In STOC’06: Proceedings of the 38th Annual ACM Symposium on Theory of Computing , 261–270. ACM, New York, 2006
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C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós and K. Vesztergombi, Counting graph homomorphisms. In Topics in Discrete Mathematics (ed. M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas, P. Valtr), 315–371. Springer, New York, 2006
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L. Lovász, The rank of connection matrices and the dimension of graph algebras. Eur. J. Comb. 27
2006
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L. Lovász and B. Szegedy, Limits of dense graph sequences. J . Comb. Theory B 96
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B. Bollobás, S. Janson and O. Riordan, The phase transition in inhomogeneous random graphs. Random Struct. Alg. 31
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B. Bollobás and O. Riordan, Sparse graphs: metrics and random models. Preprint, 2007. http://arxiv.org/0708.1919v1
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C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós and K. Vesztergombi, Convergent sequences of dense graphs II: Multiway cuts and statistical physics. Preprint, 2007. http://research.microsoft.com/ ∼ \sim borgs/
2007
Closest in time.
M. Freedman, L. Lovász and A. Schrijver, Reflection positivity, rank connectivity, and homomorphism of graphs. J. Amer. Math. Soc. 20
2007
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L. Lovász, Connection matrices. In Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh (ed. G. Grimmet and C. McDiarmid), 179–190. Oxford University Press, Oxford, 2007
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L. Lovász and B. Szegedy, Szemerédi’s Lemma for the analyst. J. Geom. Func. Anal. 17
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L. Lovász and B. Szegedy, Testing properties of graphs and functions. Preprint, 2007
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C. Borgs, J. T. Chayes, L. Lovász, V. T. Sós and K. Vesztergombi, Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing. Preprint, 2007. http://arxiv.org/math.CO/0702004
2007
Cited alongside, same era.
C. Borgs, J. T. Chayes and L. Lovász, Unique limits of dense graph sequences. In preparation
Cited in the paper.
P. Diaconis, S. Holmes and S. Janson, Threshold graph limits and random threshold graphs. In preparation
Cited in the paper.
L. Lovász and B. Szegedy, Contractors and connectors in graph algebras. J. Comb. Theory B , to appear
Cited in the paper.
L. Lovász and V. T. Sós, Generalized quasirandom graphs. J. Comb. Theory B. 98
2008
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