dc.contributor.author | Abrishami, Tara | |
dc.contributor.author | Chudnovsky, Maria | |
dc.contributor.author | Dibek, Cemil | |
dc.contributor.author | Hajebi, Sepehr | |
dc.contributor.author | Rzqzewski, Pawel | |
dc.contributor.author | Spirkl, Sophie | |
dc.contributor.author | Vuskovic, Kristina | |
dc.date.accessioned | 2023-11-21 15:40:24 (GMT) | |
dc.date.available | 2023-11-21 15:40:24 (GMT) | |
dc.date.issued | 2024-01 | |
dc.identifier.uri | https://doi.org/10.1016/j.jctb.2023.10.005 | |
dc.identifier.uri | http://hdl.handle.net/10012/20107 | |
dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.jctb.2023.10.005 © 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 | This paper is motivated by the following question: what are the unavoidable induced
subgraphs of graphs with large treewidth? Aboulker et al. made a conjecture which
answers this question in graphs of bounded maximum degree, asserting that for all k and Δ,
every graph with maximum degree at most Δ and sufficiently large treewidth contains either
a subdivision of the (k × k)-wall or the line graph of a subdivision of the (k × k)-wall as an
induced subgraph. We prove two theorems supporting this conjecture, as follows.
1. For t ≥ 2, a t-theta is a graph consisting of two nonadjacent vertices and three internally
vertex-disjoint paths between them, each of length at least t. A t-pyramid is a graph
consisting of a vertex v, a triangle B disjoint from v and three paths starting at v and
vertex-disjoint otherwise, each joining v to a vertex of B, and each of length at least
t. We prove that for all k, t and Δ, every graph with maximum degree at most Δ and
sufficiently large treewidth contains either a t-theta, or a t-pyramid, or the line graph of
a subdivision of the (k × k)-wall as an induced subgraph. This affirmatively answers a
question of Pilipczuk et al. asking whether every graph of bounded maximum degree and
sufficiently large treewidth contains either a theta or a triangle as an induced subgraph
(where a theta means a t-theta for some t ≥ 2).
2. A subcubic subdivided caterpillar is a tree of maximum degree at most three whose all
vertices of degree three lie on a path. We prove that for every Δ and subcubic subdivided
caterpillar T, every graph with maximum degree at most Δ and sufficiently large treewidth
contains either a subdivision of T or the line graph of a subdivision of T as an induced
subgraph. | en |
dc.description.sponsorship | NSF, Grant DMS-1763817 || NSF-EPSRC, Grant DMS-2120644 || 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 II. Toward walls and their line graphs in graphs of bounded degree. | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Abrishami, T., Chudnovsky, M., Dibek, C., Hajebi, S., Rzążewski, P., Spirkl, S., & Vušković, K. (2024). Induced subgraphs and tree decompositions II. toward walls and their line graphs in graphs of bounded degree. Journal of Combinatorial Theory, Series B, 164, 371–403. https://doi.org/10.1016/j.jctb.2023.10.005 | 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 |