https://m2.mtmt.hu/ eng 2026-04-16 23:33 JournalArticle 33106524 ADMIN_APPROVED true Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, 30-348, Poland Faculty of Informatics, Masaryk University, Botanická 68A, Brno, 602 00, Czech Republic Mathematics Institute, DIMAP and Department of Computer Science, University of Warwick, Coventry, CV4 7AL, United Kingdom Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, Prague, 120 00, Czech Republic Cited By :3 Export Date: 18 January 2024 CODEN: JCBTB Funding details: MUNI/I/1677/2018 Funding details: National Science Foundation, NSF, DMS-1705204 Funding details: European Research Council, ERC Funding details: Horizon 2020, 648509 Funding details: Masarykova Univerzita, MU Funding text 1: The work of the first, second and last authors has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 648509 ). The second and the last were also supported by the MUNI Award in Science and Humanities ( MUNI/I/1677/2018 ) of the Grant Agency of Masaryk University . The work of the third author was supported by NSF Postdoctoral Fellowship Award DMS-1705204 . This publication reflects only its authors' view; the European Research Council Executive Agency is not responsible for any use that may be made of the information it contains. Funding text 2: The work of the first, second and last authors has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 648509). The second and the last were also supported by the MUNI Award in Science and Humanities (MUNI/I/1677/2018) of the Grant Agency of Masaryk University. The work of the third author was supported by NSF Postdoctoral Fellowship Award DMS-1705204. This publication reflects only its authors' view; the European Research Council Executive Agency is not responsible for any use that may be made of the information it contains. 0 false 2025-12-31T19:27:49.849+0000 2024-02-26T15:35:44.421+0000 2022-09-22T10:27:27.957+0000 true 10071503 Szabó Regina /api/admin/10071503 Admin true 2024-05-14T18:07:19.620+0000 2024-02-26T15:35:44.644+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 Grzesik, A. Cycles of a given length in tournaments true true /api/journal/2387 REVIEWED true false 2387 false 2387 true 0095-8956 1096-0902 Journal FOREIGN 158 117 145 117 29 2022 We study the asymptotic behavior of the maximum number of directed cycles of a given length in a tournament: let c(l) be the limit of the ratio of the maximum number of cycles of length l in an n-vertex tournament and the expected number of cycles of length l in the random n-vertex tournament, when n tends to infinity. It is well-known that c(3) = 1 and c(4) = 4/3. We show that c(l) = 1 if and only if l is not divisible by four, which settles a conjecture of Bartley and Day. If l is divisible by four, we show that 1 + 2 center dot (2/pi)(l) <= c(l) <= 1 + (2/pi+ o(1))(l) and determine the value c(l) exactly for l = 8. We also give a full description of the asymptotic structure of tournaments with the maximum number of cycles of length l when l is not divisible by four or l is an element of{4, 8}. (c) 2022 Elsevier Inc. All rights reserved. 2022 true true true false false NONE 2025-12-31 false 6 0 6 3 0 6 6 4 6 6 6 3 3 3 3 0 6 3 6 3 0 2 2 Folyóiratcikk Journal Article 24 6 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 0 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 2022 0 1 0 1 0 2023 0 2 1 2 1 2024 0 0 0 0 0 2025 0 3 2 3 2 D1 false false false false 2022-12-21T11:52:13.325+0000 1 14 0 4 0 true Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 103497273 /api/authorship/103497273 1 0.25 true false false Grzesik A. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 103497274 /api/authorship/103497274 2 0.25 false false false Král' D. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 103497275 /api/authorship/103497275 3 0.25 false false false Author 10000916 /api/author/10000916 Lovász László true 10000916 true Lovász L.M. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 103497276 /api/authorship/103497276 4 0.25 false true false Volec J. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 21715198 /api/publicationidentifier/21715198 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1016/j.jctb.2022.07.007 https://doi.org/10.1016/j.jctb.2022.07.007 false true PublicationIdentifier 23717531 /api/publicationidentifier/23717531 PlainSource 1 /api/publicationsource/1 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 000901805500006 https://www.webofscience.com/wos/woscc/full-record/000901805500006 false true PublicationIdentifier 21715197 /api/publicationidentifier/21715197 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true IDENTICAL 85135537488 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85135537488 false true SjrRating 11290595 /api/sjrrating/11290595 13 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 1703 /api/classificationexternal/1703 true 1703 true D1 DIRECT true true /api/publication/33106524 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" >Grzesik A. </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Král' D. </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10000916"><a href="/gui2/?type=authors&mode=browse&sel=10000916" target="_blank">Lovász L.M. (<span class="authorship-author-name">Lovász László</span> <span class="authorAux-mtmt"> Matematika, számítógéptudomány</span>) </a> </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Volec J. </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33106524" target="_blank">Cycles of a given length in tournaments</a></div> <div> <span class="journal-title">JOURNAL OF COMBINATORIAL THEORY SERIES B</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0095-8956">0095-8956</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1096-0902">1096-0902</a>)</span>: <span class="journal-volume">158</span> <span class="page"> pp 117-145 </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="10.1016/j.jctb.2022.07.007" target="_blank" href="https://doi.org/10.1016/j.jctb.2022.07.007"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000901805500006" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000901805500006"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85135537488" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85135537488"> Scopus </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Journal subject: Scopus - Computational Theory and Mathematics&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> <div class="journal-subject">Journal subject: Scopus - Discrete Mathematics and Combinatorics&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> <div class="journal-subject">Journal subject: Scopus - Theoretical Computer Science&nbsp;&nbsp;&nbsp;Rank:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="" class="citingPub-count">Citing papers: 6</span> | Independent citation: 3 | Self citation: 3 | Unknown citation: 0 | Number of citations in WoS: 4 | Number of citations in Scopus:&nbsp;6 | WoS/Scopus assigned:&nbsp;6 | Number of citations with DOI:&nbsp;6 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33106524&sort=publishedYear,desc&sort=title"> Number of cited publications: 2 </a> </div> <div class="mtid"><span class="long-pub-mtid">Publication: 33106524</span> | <span class="status-data status-ADMIN_APPROVED"> Admin approved </span> Core Citing | <span class="type-subtype">Journal Article ( Article ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Last Modified: 2024.02.26. 16:35 Erzsebet Szakonyi (RAMKI admin 4) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Comments</u>: Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, 30-348, Poland Faculty of Informatics, Masaryk University, Botanická 68A, Brno, 602 00, Czech Republic Mathematics Institute, DIMAP and Department of Computer Science, University of Warwick, Coventry, CV4 7AL, United Kingdom Depart...</pre> </div></div>