Graphs of low average degree without independent transversals

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dc.contributor.authorGroenland, Carla
dc.contributor.authorKaiser, Tomáš
dc.contributor.authorTreffers, Oscar
dc.contributor.authorWales, Matthew
dc.date.accessioned2023-01-30T11:00:33Z
dc.date.available2023-01-30T11:00:33Z
dc.date.issued2023
dc.description.abstract-translatedAn independent transversal of a graph G with a vertex partition P is an independent set of G intersecting each block of P in a single vertex. Wanless and Wood proved that if each block of P has size at least t and the average degree of vertices in each block is at most t/4, then an independent transversal of P exists. We present a construction showing that this result is optimal: for any ε>0 and sufficiently large t, there is a family of forests with vertex partitions whose block size is at least t, average degree of vertices in each block is at most (1/4+ε)t, and there is no independent transversal. This unexpectedly shows that methods related to entropy compression such as the Rosenfeld-Wanless-Wood scheme or the Local Cut Lemma are tight for this problem. Further constructions are given for variants of the problem, including the hypergraph version.en
dc.format14 s.cs
dc.format.mimetypeapplication/pdf
dc.identifier.citationGROENLAND, C. KAISER, T. TREFFERS, O. WALES, M. Graphs of low average degree without independent transversals. Journal of Graph Theory, 2023, roč. 102, č. 2, s. 374-387. ISSN: 0364-9024cs
dc.identifier.document-number841136400001
dc.identifier.doi10.1002/jgt.22876
dc.identifier.issn0364-9024
dc.identifier.obd43937771
dc.identifier.uri2-s2.0-85135964681
dc.identifier.urihttp://hdl.handle.net/11025/51215
dc.language.isoenen
dc.project.IDGA20-09525S/Strukturální vlastnosti tříd grafů charakterizovaných zakázanými indukovanými podgrafycs
dc.publisherWileyen
dc.relation.ispartofseriesJournal of Graph Theoryen
dc.rights© authorsen
dc.rights.accessopenAccessen
dc.subject.translatedindependent transversalen
dc.subject.translatedLovász Local Lemmaen
dc.subject.translatedentropy compressionen
dc.titleGraphs of low average degree without independent transversalsen
dc.typečlánekcs
dc.typearticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen

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