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dc.contributor.authorAbrishami, Tara
dc.contributor.authorAlecu, Bogdan
dc.contributor.authorChudnovsky, Maria
dc.contributor.authorHajebi, Sepehr
dc.contributor.authorSpirkl, Sophie 15:40:14 (GMT) 15:40:14 (GMT)
dc.descriptionThe final publication is available at Elsevier via © 2024. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractWe say a class C of graphs is clean if for every positive integer t there exists a positive integer w(t) such that every graph in C with treewidth more than w(t) contains an induced subgraph isomorphic to one of the following: the complete graph Kt, the complete bipartite graph Kt,t, a subdivision of the (t × t)-wall or the line graph of a subdivision of the (t × t)-wall. In this paper, we adapt a method due to Lozin and Razgon (building on earlier ideas of Weißauer) to prove that the class of all H-free graphs (that is, graphs with no induced subgraph isomorphic to a fixed graph H) is clean if and only if H is a forest whose components are subdivided stars. Their method is readily applied to yield the above characterization. However, our main result is much stronger: for every forest H as above, we show that forbidding certain connected graphs containing H as an induced subgraph (rather than H itself) is enough to obtain a clean class of graphs. Along the proof of the latter strengthening, we build on a result of Davies and produce, for every positive integer η, a complete description of unavoidable connected induced subgraphs of a connected graph G containing η vertices from a suitably large given set of verticen
dc.description.sponsorshipNSF-EPSRC, Grant DMS-2120644 || AFOSR, Grant FA9550-22-1-0083 || DMS-EPSRC, Grant EP/V002813/1 || NSERC, RGPIN-2020-03912.en
dc.relation.ispartofseriesJournal of Combinatorial Theory, Series B;164
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectinduced subgraphen
dc.subjecttree decompositionen
dc.titleInduced subgraphs and tree decompositions VII. Basic obstructions in H-free graphs.en
dcterms.bibliographicCitationAbrishami, T., Alecu, B., Chudnovsky, M., Hajebi, S., & Spirkl, S. (2024). Induced subgraphs and tree decompositions VII. basic obstructions in H-free graphs. Journal of Combinatorial Theory, Series B, 164, 443–472.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen

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