Induced subgraphs and tree decompositions VI. Graphs with 2-cutsets

dc.contributor.authorAbrishami, Tara
dc.contributor.authorChudnovsky, Maria
dc.contributor.authorHajebi, Sepehr
dc.contributor.authorSpirkl, Sophie
dc.date.accessioned2024-10-23T18:34:26Z
dc.date.available2024-10-23T18:34:26Z
dc.date.issued2025-01
dc.descriptionThe final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2024.114195. © 2025. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.description.abstractThis paper continues a series of papers investigating the following question: which hereditary graph classes have bounded treewidth? We call a graph t-clean if it does not contain as an induced subgraph the complete graph Kt, the complete bipartite graph Kt,t, subdivisions of a (t x t)-wall, and line graphs of subdivisions of a (t x t)-wall. It is known that graphs with bounded treewidth must be t-clean for some t; however, it is not true that every t-clean graph has bounded treewidth. In this paper, we show that three types of cutsets, namely clique cutsets, 2-cutsets, and 1-joins, interact well with treewidth and with each other, so graphs that are decomposable by these cutsets into basic classes of bounded treewidth have bounded treewidth. We apply this result to two hereditary graph classes, the class of (ISK4, well)-free graphs and the class of graphs with no cycle with a unique chord. These classes were previously studied and decomposition theorems were obtained for both classes. Our main results are that t-clean (ISK4, wheel)-free graphs have bounded treewidth and that t-clean graphs with no cycle with a unique chord have bounded treewidth.
dc.description.sponsorshipNSF, Grant DMS-1763817 || NSF-EPSRC, Grant DMS-2120644 || NSERC, RGPIN-2020-03912.
dc.identifier.urihttps://doi.org/10.1016/j.disc.2024.114195
dc.identifier.urihttps://hdl.handle.net/10012/21162
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofseriesDiscrete Mathematics; 348(1); 114195
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjecttreewidth
dc.subjectinduced subgraphs
dc.subjecttree decompositions
dc.titleInduced subgraphs and tree decompositions VI. Graphs with 2-cutsets
dc.typeArticle
dcterms.bibliographicCitationAbrishami, T., Chudnovsky, M., Hajebi, S., & Spirkl, S. (2025). Induced subgraphs and tree decompositions VI. graphs with 2-cutsets. Discrete Mathematics, 348(1), 114195. https://doi.org/10.1016/j.disc.2024.114195
uws.contributor.affiliation1Faculty of Mathematics
uws.contributor.affiliation2Combinatorics and Optimization
uws.peerReviewStatusReviewed
uws.scholarLevelFaculty
uws.typeOfResourceTexten

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