On 1-factors with prescribed lengths in tournaments

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dc.contributor.authorKang, Dong Yeapko
dc.contributor.authorKim, Jaehoonko
dc.date.accessioned2020-02-05T02:20:05Z-
dc.date.available2020-02-05T02:20:05Z-
dc.date.created2020-02-04-
dc.date.created2020-02-04-
dc.date.created2020-02-04-
dc.date.created2020-02-04-
dc.date.created2020-02-04-
dc.date.issued2020-03-
dc.identifier.citationJOURNAL OF COMBINATORIAL THEORY SERIES B, v.141, no.1, pp.31 - 71-
dc.identifier.issn0095-8956-
dc.identifier.urihttp://hdl.handle.net/10203/272065-
dc.description.abstractWe prove that every strongly 10(50)t-connected tournament contains all possible 1-factors with at most t components and this is best possible up to constant. In addition, we can ensure that each cycle in the 1-factor contains a prescribed vertex. This answers a question by Kuhn, Osthus, and Townsend. Indeed, we prove more results on partitioning tournaments. We prove that a strongly Omega(k(4)tq)-connected tournament admits a vertex partition into t strongly k-connected tournaments with prescribed sizes such that each tournament contains q prescribed vertices, provided that the prescribed sizes are Omega(n). This result improves the earlier result of Kuhn, Osthus, and Townsend. We also prove that for a strongly Omega(t)-connected n-vertex tournament T and given 2t distinct vertices x(1), ... , x(t), y(1), ... , y(t) of T, we can find t vertex disjoint paths P-1, ... , P-t such that each path P-i connecting x(i) and y(i) has the prescribed length, provided that the prescribed lengths are Omega(n). For both results, the condition of connectivity being linear in t is best possible, and the condition of prescribed sizes being Omega(n) is also best possible.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleOn 1-factors with prescribed lengths in tournaments-
dc.typeArticle-
dc.identifier.wosid000508288900002-
dc.identifier.scopusid2-s2.0-85068218658-
dc.type.rimsART-
dc.citation.volume141-
dc.citation.issue1-
dc.citation.beginningpage31-
dc.citation.endingpage71-
dc.citation.publicationnameJOURNAL OF COMBINATORIAL THEORY SERIES B-
dc.identifier.doi10.1016/j.jctb.2019.06.003-
dc.contributor.localauthorKim, Jaehoon-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorTournament-
dc.subject.keywordAuthorConnectivity-
dc.subject.keywordAuthor1-factor-
dc.subject.keywordAuthorCycle-
dc.subject.keywordAuthorGraph partition-
dc.subject.keywordPlusCOMPLEMENTARY CYCLES-
dc.subject.keywordPlusVERTICES-
dc.subject.keywordPlusGRAPHS-
dc.subject.keywordPlusCONNECTIVITY-
dc.subject.keywordPlusCONJECTURE-
dc.subject.keywordPlusPARTITION-
dc.subject.keywordPlusPROOF-
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