Pure pairs. II. Excluding all subdivisions of a graph
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Scott, Alex | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-08-11 23:26:02 (GMT) | |
| dc.date.available | 2022-08-11 23:26:02 (GMT) | |
| dc.date.issued | 2021-06-01 | |
| dc.identifier.uri | https://doi.org/10.1007/s00493-020-4024-1 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18505 | |
| dc.description | This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: https://doi.org/10.1007/s00493-020-4024-1 | en |
| dc.description.abstract | We prove for every graph H there exists ɛ > 0 such that, for every graph G with |G|≥2, if no induced subgraph of G is a subdivision of H, then either some vertex of G has at least ɛ|G| neighbours, or there are two disjoint sets A, B ⊆ V(G) with |A|,|B|≥ɛ|G| such that no edge joins A and B. It follows that for every graph H, there exists c>0 such that for every graph G, if no induced subgraph of G or its complement is a subdivision of H, then G has a clique or stable set of cardinality at least |G|c. This is related to the Erdős-Hajnal conjecture. | 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, AFOSR grant A9550-19-1-0187, and NSF grants DMS-1265563 and DMS-1800053. | en |
| dc.language.iso | en | en |
| dc.publisher | Springer Nature | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | pure pairs | en |
| dc.subject | Erdos-Hanjnal conjecture | en |
| dc.title | Pure pairs. II. Excluding all subdivisions of a graph | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Chudnovsky, M., Scott, A., Seymour, P., & Spirkl, S. (2021). Pure Pairs. II. Excluding All Subdivisions of A Graph. Combinatorica, 41(3), 379–405. https://doi.org/10.1007/s00493-020-4024-1 | 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 |
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