Perfect matchings in highly cyclically connected regular graphs

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dc.contributor.authorLukoťka, Robert
dc.contributor.authorRollová, Edita
dc.date.accessioned2022-04-04T10:00:11Z
dc.date.available2022-04-04T10:00:11Z
dc.date.issued2022
dc.description.abstract-translatedA leaf matching operation on a graph consists of removing a vertex of degree 1 together with its neighbour from the graph. Let G be a d‐regular cyclically (d k − 1+2 )‐ edge‐connected graph of even order, where k ≥ 0 and d ≥ 3. We prove that for any given set X of d k − 1 + edges, there is no 1‐factor of G avoiding X if and only if either an isolated vertex can be obtained by a series of leaf matching operations in G − X, or G − X has an independent set that contains more than half of the vertices of G. To demonstrate how to check the conditions of the theorem we prove several statements on 2‐factors of cubic graphs. For k ≥ 3, we prove that given a cyclically (4k − 5)‐edge‐connected cubic graphG and three paths of length k such that the distance between any two of them is at least 8k − 16, there is a 2‐factor of G that contains one of the paths. We provide a similar statement for two paths when k = 3 and k = 4. As a corollary we show that given a vertex v in a cyclically 7‐edge‐connected cubic graph, there is a 2‐factor such that v is in a circuit of length greater than 7.en
dc.format22 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationLUKOŤKA, R. ROLLOVÁ, E. Perfect matchings in highly cyclically connected regular graphs. JOURNAL OF GRAPH THEORY, 2022, roč. 100, č. 1, s. 28-49. ISSN: 0364-9024cs
dc.identifier.document-number710868900001
dc.identifier.doi10.1002/jgt.22764
dc.identifier.issn0364-9024
dc.identifier.obd43935192
dc.identifier.uri2-s2.0-85118139855
dc.identifier.urihttp://hdl.handle.net/11025/47312
dc.language.isoenen
dc.project.IDLO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnostcs
dc.project.IDEE2.3.30.0038/Nová excelence lidských zdrojůcs
dc.publisherWileyen
dc.relation.ispartofseriesJournal Of Graph Theoryen
dc.rightsPlný text není přístupný.cs
dc.rights© Wileyen
dc.rights.accessclosedAccessen
dc.subject.translated2‐factoren
dc.subject.translatedcyclic connectivityen
dc.subject.translatedperfect matchingen
dc.subject.translatedregular graphen
dc.titlePerfect matchings in highly cyclically connected regular graphsen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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