https://m2.mtmt.hu/ hun 2026-04-30 17:55 JournalArticle 3292417 APPROVED true Cited By :3 Export Date: 9 January 2019 Funding Agency and Grant Number: Marie Sklodowska-Curie [750857]; ERC [306493, 648017]; MTA Renyi "Lendulet" Groups and Graphs Research Group Funding text: We are indebted to Miklos Abert for introducing the problem to us and for his constant encouragement. We would also like to thank him and Tamas Terpai for valuable discussions and their kind permission to include the proof of Theorem 1.2 in this paper. Endre Csoka was supported by Marie Sklodowska-Curie grant 750857, ERC grants 306493 and 648017. Both authors were supported by the MTA Renyi "Lendulet" Groups and Graphs Research Group. Cited By :3 Export Date: 16 July 2020 0 2018-07-02T22:23:08.000+0000 false 3292417 2026-02-17T12:25:05.145+0000 2020-12-22T20:31:36.236+0000 2016-03-16T10:12:20.000+0000 true 10029947 Csóka Endre /api/author/10029947 Author true 10029947 2025-02-13T13:39:16.634+0000 2017-11-17T19:41:37.000+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 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 Csóka, Endre Invariant random perfect matchings in Cayley graphs true true /api/journal/10006328 REVIEWED true false 10006328 false 10006328 true 1661-7207 1661-7215 Journal FOREIGN 11 1 211 243 211 33 2017 We prove that every non-amenable Cayley graph admits a factor of IID perfect matching. We also show that any connected d-regular vertex transitive graph admits a perfect matching. The two results together imply that every Cayley graph admits an invariant random perfect matching. A key step in the proof is a result on graphings that also applies to finite graphs. The finite version says that for any partial matching of a finite regular graph that is a good expander, one can always find an augmenting path whose length is poly-logarithmic in one over the ratio of unmatched vertices. © European Mathematical Society. 2017 786381 true true true false true false GREEN GREEN 2026-02-17 true http://real.mtak.hu/44112 12 0 10 8 3 10 11 9 10 10 10 8 8 10 2 0 12 10 10 8 0 3 3 Folyóiratcikk Journal Article 24 10 Könyvrészlet Chapter in Book 25 0 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 2 Egyéb Miscellaneous 29 0 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 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2016 0 1 0 1 0 2017 0 0 0 0 0 2018 0 3 3 3 3 2019 0 3 2 3 2 2020 0 2 2 2 2 2021 0 1 1 1 1 2022 0 0 0 0 0 2023 0 0 0 0 0 2024 0 2 2 2 2 D1 true 10029947 false false false 2017-11-17T19:41:37.000+0000 2017-11-17T19:40:39.000+0000 Lendület Struktúrák Limeszei Kutatócsoport (HRN RAMKI); 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<span class="author-name" mtid="10028138"><a href="/gui2/?type=authors&mode=browse&sel=10028138" target="_blank">Lippner Gábor (<span class="authorship-author-name">Lippner Gábor</span> <span class="authorAux-mtmt"> mat</span>) </a> </span> <span class="author-affil">MTA Rényi Alfréd Matematikai Kutatóintézet; <span title="Eötvös Loránd Tudományegyetem">ELTE</span>/<span title="Természettudományi Kar">TTK</span>/Matematika Doktori Iskola</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;3292417" target="_blank">Invariant random perfect matchings in Cayley graphs</a></div> <div> <span class="journal-title">GROUPS GEOMETRY AND DYNAMICS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1661-7207">1661-7207</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1661-7215">1661-7215</a>)</span>: <span class="journal-volume">11</span> <span class="journal-issue">1</span> <span class="page"> pp 211-243 </span> <span class="year">(2017)</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="10.4171/GGD/395" target="_blank" href="https://doi.org/10.4171/GGD/395"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="44112" target="_blank" href="http://real.mtak.hu/44112"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000399725800011" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000399725800011"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85019872240" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019872240"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="MR3641840" target="_blank" href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR3641840"> Mathematical Reviews </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="1211.2374" target="_blank" href="http://arxiv.org/abs/1211.2374"> arXiv </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Discrete Mathematics and Combinatorics&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Geometry and Topology&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 12</span> | Független: 10 | Függő: 2 | Nem jelölt: 0 | WoS jelölt: 9 | Scopus jelölt:&nbsp;10 | WoS/Scopus jelölt:&nbsp;10 | DOI jelölt:&nbsp;11 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;3292417&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 3 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 3292417</span> | <span class="status-data status-APPROVED"> Nyilvános </span> <span class="oldId">Régi azonosító: 3292417</span> | Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2020.12.22. 21:31 Szuper Admin (admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Cited By :3 Export Date: 9 January 2019 Funding Agency and Grant Number: Marie Sklodowska-Curie [750857]; ERC [306493, 648017]; MTA Renyi "Lendulet" Groups and Graphs Research Group Funding text: We are indebted to Miklos Abert for introducing the problem to us and for his constant encouragement. We would also like to thank him and Tamas Terpai for valuable d...</pre> </div></div>