On a question of Vera T. Sós about size forcing of graphons

https://m2.mtmt.hu/ hun 2026-06-14 18:46 true true 1 2 2 20 100 1 2 DESC publishedYear false ASC firstAuthor true ASC title true 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 Toroczkai Annamária (idézők, admin) true 5101094 2025-03-12T11:38:52.123+0000 2025-03-12T11:38:54.944+0000 Admin 10084481 /api/admin/10084481 Toroczkai Annamária (idézők, admin) Toroczkai Annamária true true 2025-03-12T11:38:55.014+0000 false false true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType Folyóiratcikk 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType Szakcikk (Folyóiratcikk) 101 true 10000059 true 1 /api/category/1 Category Tudományos true 1 Cooley, O. On a question of Vera T. Sós about size forcing of graphons 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 Angol 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 Szerző 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 Szerző 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 Szerző 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 /api/publication/33688473 Cooley O. et al. On a question of Vera T. Sós about size forcing of graphons. (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> ;    <span class="author-name" >Kang M. </span> ;    <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">Nyelv: Angol | </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"> Idézett közlemények száma: 11 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33688473</span> | <span class="status-data status-APPROVED"> Nyilvános </span> Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="notDuplums"><a target="_blank" href="/api/publication/33688473/notduplums">1 Nem duplumnak jelölés</a> </div> <div class="lastModified">Utolsó módosítás: 2024.10.04. 10:08 Tomcsányi Zsuzsanna (MTMT_KP_admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</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> BookChapter 33103071 APPROVED true 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 0 false 2025-03-12T11:43:22.250+0000 2024-10-04T08:06:52.609+0000 2022-09-20T19:07:08.481+0000 true 10071503 Szabó Regina /api/admin/10071503 Admin Szabó Regina (ELTE TTK admin 5) true 2025-03-12T11:38:58.213+0000 2025-03-12T11:38:58.213+0000 false false true 25 25 /api/publicationtype/25 PublicationType Könyvrészlet 2 true 25 BookChapter true 10000398 Chapter true 25 25 /api/publicationtype/25 PublicationType Könyvrészlet 2 true 25 BookChapter /api/subtype/10000398 Könyvfejezet SubType Könyvfejezet (Könyvrészlet) 220 true 10000398 true 1 /api/category/1 Category Tudományos true 1 Cooley, O. 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Singularities and Their Interaction with Geometry and Low Dimensional Topology: In Honor of András Némethi. 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On a Question of Vera T. Sós About Size Forcing of Graphons. (2021) Megjelent: Singularities and Their Interaction with Geometry and Low Dimensional Topology pp. 625-630<div class="BookChapter 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> ;    <span class="author-name" >Kang M. </span> ;    <span class="author-name" >Pikhurko O. </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33103071" target="_blank">On a Question of Vera T. Sós About Size Forcing of Graphons</a></div> <div class="InBook"><div class="chapter-in">In:</div> <div class="authors"> <div class="autype autype-1"> <span class="author-name" >Fernández de Bobadilla Javier </span> ;    <span class="author-name" mtid="10044220"><a href="/gui2/?type=authors&mode=browse&sel=10044220" target="_blank">László Tamás (<span class="authorship-author-name">László Tamás</span> <span class="authorAux-mtmt"> Szingularitás elmélet</span>) </a> </span> ;    <span class="author-name" >Stipsicz András </span> (szerk.) </div> </div> <div class="booktitle"><a href="/gui2/?mode=browse&params=publication;32727412" target="_blank">Singularities and Their Interaction with Geometry and Low Dimensional Topology : In Honor of András Némethi </a></div> <span class="publishedAt">Cham: <span class="publishers">Birkhäuser Verlag Basel</span>, <span class="page"> pp 625-630 </span> <span class="year">(2021)</span> ( <span class="seriesTitle">Trends in Mathematics</span> <span class="issn">2297-0215</span> <span class="issn">2297-024X</span> ) </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="10.1007/978-3-030-83823-2_100" target="_blank" href="https://doi.org/10.1007/978-3-030-83823-2_100"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85114106342" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85114106342"> Scopus </a> </span> </span> <span class="bookchapter-ids">Befoglaló link(ek):</span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="10.1007/978-3-030-61958-9" target="_blank" href="https://doi.org/10.1007/978-3-030-61958-9"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <span class="isbnOrIssn"> ISBN: </span> <a style="color:black" title="9783030619572" target="_blank" href="https://www.worldcat.org/search?q=isbn%3A9783030619572"> 9783030619572 </a> </span> <span class="id identifier oa_none" title="none"> <span class="isbnOrIssn"> ISBN: </span> <a style="color:black" title="9783030619589" target="_blank" href="https://www.worldcat.org/search?q=isbn%3A9783030619589"> 9783030619589 </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="https://link.springer.com/10.1007/978-3-030-61958-9" target="_blank" href="https://link.springer.com/10.1007/978-3-030-61958-9"> Egyéb URL </a> </span> </span> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33103071&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 2 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33103071</span> | <span class="status-data status-APPROVED"> Nyilvános </span> <span class="long-book-mtid">Befoglaló: 32727412</span> Idéző | <span class="type-subtype">Könyvrészlet ( Könyvfejezet ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="notDuplums"><a target="_blank" href="/api/publication/33103071/notduplums">6 Nem duplumnak jelölés</a> </div> <div class="lastModified">Utolsó módosítás: 2024.10.04. 10:06 Tomcsányi Zsuzsanna (MTMT_KP_admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: 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; emai...</pre> </div> </div>