Pure pairs. I. Trees and linear anticomplete pairs
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-08-12T00:57:03Z | |
| dc.date.available | 2022-08-12T00:57:03Z | |
| dc.date.issued | 2020-12-02 | |
| dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.aim.2020.107396. © 2020. 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 | The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this paper, we prove a conjecture of Liebenau and Pilipczuk [11], that for every forest H there exists c > 0, such that every graph G with |G| > 1 contains either an induced copy of H, or a vertex of degree at least c|Gj|, or two disjoint sets of at least c|G| vertices with no edges between them. It follows that for every forest H there exists c > 0 such that, if G contains neither H nor its complement as an induced subgraph, then there is a clique or stable set of cardinality at least |G|c. | en |
| dc.description.sponsorship | Supported by NSF grant DMS-1550991. This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number W911NF-16-1-0404. Supported by a Leverhulme Trust Research Fellowship. Supported by ONR grant N00014-14-1-0084, and NSF grant DMS-1265563, and AFOSR grant A9550-19-1-0187. This work was mostly performed while Spirkl was at Princeton University. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.aim.2020.107396 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18524 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | Erdős-Hajnal conjecture | en |
| dc.subject | induced subgraphs | en |
| dc.subject | forests | en |
| dc.title | Pure pairs. I. Trees and linear anticomplete pairs | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Chudnovsky, M., Scott, A., Seymour, P., & Spirkl, S. (2020). Pure pairs. I. Trees and linear anticomplete pairs. Advances in Mathematics, 375, 107396. https://doi.org/10.1016/j.aim.2020.107396 | 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 |