TY  - JOUR
AU  - Csóka, Endre
TI  - On the graph limit question of Vera T. Sos
JF  - JOURNAL OF COMBINATORIAL THEORY SERIES B
J2  - J COMB THEORY B
VL  - 116
PY  - 2016
SP  - 306
EP  - 311
PG  - 6
SN  - 0095-8956
DO  - 10.1016/j.jctb.2015.09.003
UR  - https://m2.mtmt.hu/api/publication/3130076
ID  - 3130076
N1  - Funding Agency and Grant Number: ERC [306493, 648017]
            Funding text: Supported by ERC grants 306493 and 648017.
Funding Agency and Grant Number: ERCEuropean Research Council (ERC) [306493, 648017]
            Funding text: Supported by ERC grants 306493 and 648017.
Export Date: 20 July 2020            
            CODEN: JCBTB            
            Correspondence Address: Csóka, E.; Institute of Mathematics and DIMAP, University of WarwickUnited Kingdom; email: csokaendre@gmail.com
AB  - In the dense graph limit theory, the topology of the set of graphs is defined by the distribution of the subgraphs spanned by finite number of random vertices. Vera T. Sos proposed a question that if we consider only the number of edges in the spanned subgraphs, then whether it provides an equivalent definition. We show that the answer is positive on quasirandom graphs, and we prove a generalization of the statement. (C) 2015 Elsevier Inc. All rights reserved.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Borgs, C
AU  - Chayes, J
AU  - Lovász, László
TI  - MOMENTS OF TWO-VARIABLE FUNCTIONS AND THE UNIQUENESS OF GRAPH LIMITS
JF  - GEOMETRIC AND FUNCTIONAL ANALYSIS
J2  - GEOM FUNCT ANAL
VL  - 19
PY  - 2010
IS  - 6
SP  - 1597
EP  - 1619
PG  - 23
SN  - 1016-443X
DO  - 10.1007/s00039-010-0044-0
UR  - https://m2.mtmt.hu/api/publication/2149488
ID  - 2149488
N1  - Microsoft Research New England, One Memorial Drive, Cambridge, MA 02142, United States            
            Institute of Mathematics, Eötös Loránd University, Pf. 120, 1518 Budapest, Hungary            
            Cited By :73            
            Export Date: 10 June 2022            
            Correspondence Address: Lovász, L.; Institute of Mathematics, Pf. 120, 1518 Budapest, Hungary; email: lovasz@cs.elte.hu
AB  - For a symmetric bounded measurable function W on [0, 1](2) and a simple graph F, the homomorphism density t(F,W) = integral([0,1]V(F)) Pi(ij is an element of E(F)) W(x(i),x(j))dx. can be thought of as a "moment" of W. We prove that every such function is determined by its moments up to a measure preserving transformation of the variables. The main motivation for this result comes from the theory of convergent graph sequences. A sequence (G(n)) of dense graphs is said to be convergent if the probability, t(F, G(n)), that a random map from V (F) into V (G(n)) is a homomorphism converges for every simple graph F. The limiting density can be expressed as t( F, W) for a symmetric bounded measurable function W on [0, 1](2). Our results imply in particular that the limit of a convergent graph sequence is unique up to measure preserving transformation.
LA  - English
DB  - MTMT
ER  -