dc.contributor.author | Scott, Alex | |
dc.contributor.author | Seymour, Paul | |
dc.contributor.author | Spirkl, Sophie | |
dc.date.accessioned | 2022-08-18 13:33:04 (GMT) | |
dc.date.available | 2022-08-18 13:33:04 (GMT) | |
dc.date.issued | 2022-01 | |
dc.identifier.uri | https://doi.org/10.1137/20M1368331 | |
dc.description | First Published in the Journal of Discrete Mathematics in Volume 36, Issue 1, 2022, published by the
Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized
reproduction of this article is prohibited. | en |
dc.description.abstract | A pure pair in a graph G is a pair (Z1,Z2) of disjoint sets of vertices such that either every vertex in Z1 is adjacent to every vertex in Z2, or there are no edges between Z1 and Z2. With Maria Chudnovsky, we recently proved that, for every forest F, every graph G with at least two vertices that does not contain F or its complement as an induced subgraph has a pure pair (Z1,Z2) with |Z1|,|Z2| linear in |G|. Here we investigate what we can say about pure pairs in an ordered graph G, when we exclude an ordered forest F and its complement as induced subgraphs. Fox showed that there need not be a linear pure pair; but Pach and Tomon showed that if F is a monotone path, then there is a pure pair of size c|G|/log|G|. We generalize this to all ordered forests, at the cost of a slightly worse bound: we prove that, for every ordered forest F, every ordered graph G with at least two vertices that does not contain F or its complement as an induced subgraph has a pure pair of size |G|1−o(1). | en |
dc.description.sponsorship | Supported by AFOSR grant A9550-19-1-0187 and NSF grant DMS-1800053. This material is based upon work supported by the National Science Foundation under Award No. DMS-1802201. | en |
dc.language.iso | en | en |
dc.publisher | Society for Industrial and Applied Mathematics Journal on Discrete Mathematics | en |
dc.subject | pure pairs | en |
dc.title | Pure Pairs VI. Excluding an Ordered Tree. | en |
dc.type | Article | en |
dc.provenance | Two authors deleted and two new authors added by Logan Imans on 08/31/2022 at the request of Sophie Spirkl due to error in previous entry | en |
dcterms.bibliographicCitation | Scott, A., Seymour, P., & Spirkl, S. (2022). Pure Pairs VI. Excluding an Ordered Tree. SIAM Journal on Discrete Mathematics, 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 |