dc.contributor.author | Abrishami, Tara | |
dc.contributor.author | Alecu, Bogdan | |
dc.contributor.author | Chudnovsky, Maria | |
dc.contributor.author | Hajebi, Sepehr | |
dc.contributor.author | Spirkl, Sophie | |
dc.date.accessioned | 2023-11-21 15:40:14 (GMT) | |
dc.date.available | 2023-11-21 15:40:14 (GMT) | |
dc.date.issued | 2024-01 | |
dc.identifier.uri | https://doi.org/10.1016/j.jctb.2023.10.008 | |
dc.identifier.uri | http://hdl.handle.net/10012/20106 | |
dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2023.10.008. © 2024. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | en |
dc.description.abstract | We 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 vertic | en |
dc.description.sponsorship | NSF-EPSRC, Grant DMS-2120644 || AFOSR, Grant FA9550-22-1-0083 || DMS-EPSRC, Grant EP/V002813/1 || NSERC, RGPIN-2020-03912. | en |
dc.language.iso | en | en |
dc.publisher | Elsevier | en |
dc.relation.ispartofseries | Journal of Combinatorial Theory, Series B;164 | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | induced subgraph | en |
dc.subject | tree decomposition | en |
dc.subject | treewidth | en |
dc.title | Induced subgraphs and tree decompositions VII. Basic obstructions in H-free graphs. | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Abrishami, 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. https://doi.org/10.1016/j.jctb.2023.10.008 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Combinatorics and Optimization | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |