Pure pairs. IV. Trees in bipartite graphs.
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2023-03-31T19:27:06Z | |
| dc.date.available | 2023-03-31T19:27:06Z | |
| dc.date.issued | 2023-07 | |
| dc.description.abstract | In this paper we investigate the bipartite analogue of the strong Erd˝os-Hajnal property. We prove that for every forest H and every τ with 0 < τ ≤ 1, there exists ε > 0, such that if G has a bipartition (A,B) and does not contain H as an induced subgraph, and has at most (1− τ )|A| · |B| edges, then there is a stable set X of G with |X ∩ A| ≥ ε|A| and |X ∩ B| ≥ ε|B|. No graphs H except forests have this property. | en |
| dc.description.sponsorship | AFOSR, Grant A9550-19-1-0187, GA9550-22-1-0234 || NSF, Grant DMS-1265563, DMS-1800053, DMS-2154169 || National Science Foundation, DMS-1802201. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.jctb.2023.02.005 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19242 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | Journal of Combinatorial Theory, Series B; | |
| 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 | bipartite graph | en |
| dc.subject | tree | en |
| dc.subject | pure pair | en |
| dc.title | Pure pairs. IV. Trees in bipartite graphs. | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Scott, A., Seymour, P., & Spirkl, S. (2023). Pure pairs. iv. trees in bipartite graphs. Journal of Combinatorial Theory, Series B, 161, 120–146. https://doi.org/10.1016/j.jctb.2023.02.0 | 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 |