Borgs, C. and Chayes, J. and Lovász, László and T. Sós, Vera and Szegedy, Balázs and Vesztergombi, Katalin (2006) Graph limits and parameter testing. In: 38th Annual ACM Symposium on Theory of Computing, STOC'06. ACM Press, New York (NY), pp. 261270. ISBN 1595931341; 9781595931344

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Abstract
We define a distance of two graphs that reflects the closeness of both local and global properties, We also define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a symmetric measurable function in two variables. We use these notions of distance and graph limits to give a general theory for parameter testing. As examples, we provide short proofs of the testability of MaxCut and the recent result of Alon and Shapira about the testability of hereditary graph properties. Copyright 2006 ACM.
Item Type:  Book Section 

Uncontrolled Keywords:  Functions; Convergence of numerical methods; Numerical analysis; Parameter estimation; Computer science; Graph theory; graph homomorphism; Graph limits; Property testing; Graph limit; Distance of graphs; Convergence of graphs; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  29 Jun 2020 12:27 
Last Modified:  29 Jun 2020 12:27 
URI:  http://real.mtak.hu/id/eprint/110695 
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