Strengthening Rodl's theorem
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2023-11-21T16:32:38Z | |
| dc.date.available | 2023-11-21T16:32:38Z | |
| dc.date.issued | 2023-11 | |
| dc.description | © 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/). | en |
| dc.description.abstract | What can be said about the structure of graphs that do not contain an induced copy of some graph H? Rödl showed in the 1980s that every H-free graph has large parts that are very sparse or very dense. More precisely, let us say that a graph F on n vertices is ε-restricted if either F or its complement has maximum degree at most εn. Rödl proved that for every graph H, and every ε > 0, every H-free graph G has a linear-sized set of vertices inducing an ε-restricted graph. We strengthen Rödl’s result as follows: for every graph H, and all ε > 0, every H-free graph can be partitioned into a bounded number of subsets inducing ε-restricted graphs. | en |
| dc.description.sponsorship | U.S. Army Research Office, Grant W911NF-16-1-0404 || NSF, Grant DMS 1763817 || EPSRC, Grant EP/V007327/1 || AFOSR, Grant FA9550-22-1-0234 || AFOSR, Grant A9550-19-1-0187 || NSF, Grant DMS-2154169 || NSF, Grant DMS-1800053 || NSERC, Grant RGPIN-2020-03912. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.jctb.2023.07.004 | |
| dc.identifier.uri | http://hdl.handle.net/10012/20111 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Journal of Combinatorial Theory, Series B;163 | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | induced subgraphs | en |
| dc.subject | sparse graphs | en |
| dc.title | Strengthening Rodl's theorem | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Chudnovsky, M., Scott, A., Seymour, P., & Spirkl, S. (2023). Strengthening rödl’s theorem. Journal of Combinatorial Theory, Series B, 163, 256–271. https://doi.org/10.1016/j.jctb.2023.07.004 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |