https://m2.mtmt.hu/ eng 2026-06-24 07:08 JournalArticle 33688473 APPROVED true 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. 0 false 2025-03-12T11:41:21.221+0000 2024-10-04T08:08:07.691+0000 2023-03-08T11:49:06.752+0000 true 10084481 Toroczkai Annamária /api/admin/10084481 Admin Annamária Toroczkai (idézők, admin) true 5101094 2025-03-12T11:38:52.123+0000 2025-03-12T11:38:54.944+0000 Admin 10084481 /api/admin/10084481 Annamária Toroczkai (idézők, admin) Toroczkai Annamária true true 2025-03-12T11:38:55.014+0000 false false true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Journal Article 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Article (Journal Article) 101 true 10000059 true 1 /api/category/1 Category Scientific true 1 Cooley, O. true true /api/journal/1417120 REVIEWED ACTA MATHEMATICA HUNGARICA 0236-5294 1588-2632 true false 1417120 false 1417120 true 0236-5294 1588-2632 Journal FOREIGN 168 1 1 26 1 26 2022 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. 2023 true true true false false NONE 2025-03-12 false 0 0 0 0 0 0 0 0 0 0 0 0 11 11 Q2 false false false false 2023-06-06T10:54:46.872+0000 6 30 0 3 0 true Language 10002 /api/language/10002 English Angol English true 2 true PersonAuthorship 106951716 /api/authorship/106951716 Cooley, O. ✉ 1 0.33333334 true false true Cooley O. true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false true PersonAuthorship 106951717 /api/authorship/106951717 Kang, M. 2 0.33333334 false false false Kang M. true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false true PersonAuthorship 106951718 /api/authorship/106951718 Pikhurko, O. 3 0.33333334 false true false Pikhurko O. true false false AuthorshipType 1 /api/authorshiptype/1 Author 0 true 0 true false true PublicationIdentifier 23205747 /api/publicationidentifier/23205747 DOI: 10.1007/s10474-022-01265-8 PlainSource 6 /api/publicationsource/6 DOI PublicationSourceType 10001 /api/publicationsourcetype/10001 DOI true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1007/s10474-022-01265-8 https://doi.org/10.1007/s10474-022-01265-8 false true PublicationIdentifier 23205748 /api/publicationidentifier/23205748 WoS: 000886839900006 PlainSource 1 /api/publicationsource/1 WoS PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 000886839900006 https://www.webofscience.com/wos/woscc/full-record/000886839900006 false true PublicationIdentifier 23205793 /api/publicationidentifier/23205793 Scopus: 85142413602 PlainSource 3 /api/publicationsource/3 Scopus PublicationSourceType 10003 /api/publicationsourcetype/10003 Indexelő adatbázis false true true Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true IDENTICAL 85142413602 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142413602 false true Keyword 1113704 /api/keyword/1113704 GRAPHON true 1113704 true Keyword 2814399 /api/keyword/2814399 k-sample true true Keyword 2814400 /api/keyword/2814400 graphon forcing true true Keyword 2814401 /api/keyword/2814401 graph container true true SjrRating 11306623 /api/sjrrating/11306623 sjr:Q2 (2022) Scopus - Mathematics (miscellaneous) ACTA MATHEMATICA HUNGARICA 0236-5294 1588-2632 194 0.49 journal RatingType 10002 /api/ratingtype/10002 sjr sjr true true ClassificationExternal 2601 /api/classificationexternal/2601 Scopus - Mathematics (miscellaneous) true 2601 true Q2 DIRECT true true Reference 39162547 /api/reference/39162547 1. 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(2022) ACTA MATHEMATICA HUNGARICA 0236-5294 1588-2632 168 1 1-26<div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" >Cooley O. ✉ </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Kang M. </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Pikhurko O. </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33688473" target="_blank">On a question of Vera T. Sós about size forcing of graphons</a></div> <div> <span class="journal-title">ACTA MATHEMATICA HUNGARICA</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0236-5294">0236-5294</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1588-2632">1588-2632</a>)</span>: <span class="journal-volume">168</span> <span class="journal-issue">1</span> <span class="page"> pp 1-26 </span> <span class="year">(2022)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s10474-022-01265-8" target="_blank" href="https://doi.org/10.1007/s10474-022-01265-8"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000886839900006" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000886839900006"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85142413602" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142413602"> Scopus </a> </span> </span> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33688473&sort=publishedYear,desc&sort=title"> Number of cited publications: 11 </a> </div> <div class="mtid"><span class="long-pub-mtid">Publication: 33688473</span> | <span class="status-data status-APPROVED"> Published </span> Citing | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="notDuplums"><a target="_blank" href="/api/publication/33688473/notduplums">1 marked as not duplum</a> </div> <div class="lastModified">Last Modified: 2024.10.04. 10:08 Zsuzsanna Tomcsányi (MTMT_KP_admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Comments</u>: 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 S...</pre> </div></div>