https://m2.mtmt.hu/ eng 2026-05-25 17:15 JournalArticle 3037335 APPROVED true Funding Agency and Grant Number: European Union [TAMOP 4.2.4. A/1-11-1-2012-0001]; European Social Fund Funding text: This research was realized in the frames of TAMOP 4.2.4. A/1-11-1-2012-0001 "National Excellence Program - Elaborating and operating an inland student and researcher personal support system" The project was subsidized by the European Union and co-financed by the European Social Fund (E.Cs). Funding Agency and Grant Number: European UnionEuropean Union (EU) [TAMOP 4.2.4. A/1-11-1-2012-0001]; European Social FundEuropean Social Fund (ESF) Funding text: This research was realized in the frames of TAMOP 4.2.4. A/1-11-1-2012-0001 "National Excellence Program - Elaborating and operating an inland student and researcher personal support system" The project was subsidized by the European Union and co-financed by the European Social Fund (E.Cs). 0 2016-12-23T13:55:26.000+0000 false 3037335 2026-05-17T07:32:24.428+0000 2025-02-26T10:49:03.880+0000 2014-12-22T14:44:53.000+0000 true 10029947 Csóka Endre /api/author/10029947 Author true 10029947 2025-02-26T10:49:03.887+0000 2025-02-26T10:49:03.887+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Endre, Csóka Invariant Gaussian processes and independent sets on regular graphs of large girth true true /api/journal/2050642 REVIEWED true false 2050642 false 2050642 true 1042-9832 1098-2418 Journal FOREIGN 47 2 284 303 284 120 2015 We prove that every 3-regular, n-vertex simple graph with sufficiently large girth contains an independent set of size at least 0.4361n. (The best known bound is 0.4352n.) In fact, computer simulation suggests that the bound our method provides is about 0.438n. Our method uses invariant Gaussian processes on the d-regular tree that satisfy the eigenvector equation at each vertex for a certain eigenvalue λ. We show that such processes can be approximated by i.i.d. factors provided that |λ|≤2d-1. We then use these approximations for λ=-2d-1 to produce factor of i.i.d. independent sets on regular trees. © 2014 Wiley Periodicals, Inc. 2016 true true true false true false GREEN GREEN 2026-05-17 true http://real.mtak.hu/33612 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 50 0 40 32 10 37 41 35 38 40 40 32 32 41 9 0 50 41 40 32 0 0 0 Folyóiratcikk Journal Article 24 28 Könyvrészlet Chapter in Book 25 12 Könyv Book 23 0 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 6 Egyéb Miscellaneous 29 4 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 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false true Reference 2091165 /api/reference/2091165 8 false true Reference 2091166 /api/reference/2091166 9 false true Reference 2091167 /api/reference/2091167 10 false true Reference 2091168 /api/reference/2091168 11 false true Reference 2091169 /api/reference/2091169 12 false true Reference 2091170 /api/reference/2091170 13 false true /api/publication/3037335 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10029947"><a href="/gui2/?type=authors&mode=browse&sel=10029947" target="_blank">Endre Csóka (<span class="authorship-author-name">Csóka Endre</span> <span class="authorAux-mtmt"> matematika</span>) </a> </span> <span class="author-affil"><span title="Alfréd Rényi Institute of Mathematics">RAMKI</span>/Groups and Graphs (ERC and Lendület HAS) Research Group; <span title="Alfréd Rényi Institute of Mathematics">RAMKI</span>/Limits of Structures (Lendület HAS) research group</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10028042"><a href="/gui2/?type=authors&mode=browse&sel=10028042" target="_blank">Balázs Gerencsér (<span class="authorship-author-name">Gerencsér Balázs</span> <span class="authorAux-mtmt"> Valószínűségszámítás és statisztika</span>) </a> </span> <span class="author-affil"><span title="Alfréd Rényi Institute of Mathematics">RAMKI</span>/Probability theory and Statistics</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10015283"><a href="/gui2/?type=authors&mode=browse&sel=10015283" target="_blank">Viktor Harangi (<span class="authorship-author-name">Harangi Viktor</span> <span class="authorAux-mtmt"> gráflimeszek</span>) </a> </span> <span class="author-affil"><span title="Alfréd Rényi Institute of Mathematics">RAMKI</span>/Combinatorics and Discrete Mathematics</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10043384"><a href="/gui2/?type=authors&mode=browse&sel=10043384" target="_blank">Bálint Virág (<span class="authorship-author-name">Virág Bálint</span> <span class="authorAux-mtmt"> Algebra</span>) </a> </span> <span class="author-affil">Alfréd Rényi Institute of Mathematics</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;3037335" target="_blank">Invariant Gaussian processes and independent sets on regular graphs of large girth</a></div> <div> <span class="journal-title">RANDOM STRUCTURES & ALGORITHMS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1042-9832">1042-9832</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1098-2418">1098-2418</a>)</span>: <span class="journal-volume">47</span> <span class="journal-issue">2</span> <span class="page"> pp 284-303 </span> <span class="year">(2015)</span> </div> <div class="pub-footer"> <span class="language" 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href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3382674"> Mathematical Reviews </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Journal subject: Scopus - Computer Graphics and Computer-Aided Design&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> <div class="journal-subject">Journal subject: Scopus - Software&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> <div class="journal-subject">Journal subject: Scopus - Applied Mathematics&nbsp;&nbsp;&nbsp;Rank:&nbsp;Q1</div> <div class="journal-subject">Journal subject: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;Rank:&nbsp;Q1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 50</span> | Independent citation: 41 | Self citation: 9 | Unknown citation: 0 | Number of citations in WoS: 35 | Number of citations in Scopus:&nbsp;38 | WoS/Scopus assigned:&nbsp;40 | Number of citations with DOI:&nbsp;41 </div> <div class="mtid"><span class="long-pub-mtid">Publication: 3037335</span> | <span class="status-data status-APPROVED"> Published </span> <span class="oldId">Old id: 3037335</span> | Core | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Last Modified: 2025.02.26. 11:49 Gusztáv Ladányi (MTMT API user, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Comments</u>: Funding Agency and Grant Number: European Union [TAMOP 4.2.4. A/1-11-1-2012-0001]; European Social Fund Funding text: This research was realized in the frames of TAMOP 4.2.4. A/1-11-1-2012-0001 "National Excellence Program - Elaborating and operating an inland student and researcher personal support system" The project was subsidized by the European Union and co-financed by the Eur...</pre> </div></div>