TY  - JOUR
AU  - Cooley, O.
AU  - Kang, M.
AU  - Pikhurko, O.
TI  - On a question of Vera T. Sós about size forcing of graphons
JF  - ACTA MATHEMATICA HUNGARICA
J2  - ACTA MATH HUNG
VL  - 168
PY  - 2022
IS  - 1
SP  - 1
EP  - 26
PG  - 26
SN  - 0236-5294
DO  - 10.1007/s10474-022-01265-8
UR  - https://m2.mtmt.hu/api/publication/33688473
ID  - 33688473
N1  - Export Date: 8 March 2023            
            Correspondence Address: Cooley, O.; Institute of Science and Technology Austria (ISTA), Am Campus 1, Austria; email: oliver.cooley@ist.ac.at            
            Funding details: Leverhulme Trust, RPG-2018-424            
            Funding details: European Research Council, ERC, 101020255            
            Funding details: Austrian Science Fund, FWF, I3747            
            Funding text 1: Supported by Austrian Science Fund (FWF) Grant I3747.            
            Funding text 2: Supported by ERC Advanced Grant 101020255 and Leverhulme Research Project Grant RPG-2018-424.
AB  - The k-sampleG(k, W) from a graphon W: [ 0 , 1 ] 2→ [ 0 , 1 ] is the random graph on { 1 , … , k} , where we sample x1, … , xk∈ [ 0 , 1 ] uniformly at random and make each pair { i, j} ⊆ { 1 , … , k} an edge with probability W(xi, xj) , with all these choices being mutually independent. Let the random variable Xk(W) be the number of edges in G(k, W). Vera T. Sós asked in 2012 whether two graphons U, W are necessarily weakly isomorphic if the random variables Xk(U) and Xk(W) have the same distribution for every integer k≥ 2. This question when one of the graphons W is a constant function was answered positively by Endre Csóka and independently by Jacob Fox, Tomasz Łuczak and Vera T. Sós. Here we investigate the question when W is a 2-step graphon and prove that the answer is positive for a 3-dimensional family of such graphons. We also present some related results. © 2022, Akadémiai Kiadó, Budapest, Hungary.
LA  - English
DB  - MTMT
ER  - 

TY  - CHAP
AU  - Cooley, O.
AU  - Kang, M.
AU  - Pikhurko, O.
ED  - Fernández de Bobadilla, Javier
ED  - László, Tamás
ED  - Stipsicz, András
TI  - On a Question of Vera T. Sós About Size Forcing of Graphons
T2  - Singularities and Their Interaction with Geometry and Low Dimensional Topology
VL  - 14
PB  - Birkhäuser Verlag Basel
CY  - Cham
SN  - 9783030619589
T3  - Trends in Mathematics, ISSN 2297-0215
PY  - 2021
SP  - 625
EP  - 630
PG  - 6
DO  - 10.1007/978-3-030-83823-2_100
UR  - https://m2.mtmt.hu/api/publication/33103071
ID  - 33103071
N1  - Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, Graz, 8010, Austria            
            Mathematics Institute and DIMAP, University of Warwick, Coventry, CV4 7AL, United Kingdom            
            Export Date: 20 September 2022            
            Correspondence Address: Cooley, O.; Institute of Discrete Mathematics, Steyrergasse 30, Austria; email: cooley@math.tugraz.at
LA  - English
DB  - MTMT
ER  -