Journal article
Induced subgraphs of induced subgraphs of large chromatic number
- Abstract:
- We prove that, for every graph F with at least one edge, there is a constant such that there are graphs of arbitrarily large chromatic number and the same clique number as F in which every F-free induced subgraph has chromatic number at most cF. This generalises recent theorems of Briański, Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Our results imply that for every r ≥ 3 the class of Kr-free graphs has a very strong vertex Ramsey-type property, giving a vast generalisation of a result of Folkman from 1970. We also prove related results for tournaments, hypergraphs and infinite families of graphs, and show an analogous statement for graphs where clique number is replaced by odd girth.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 438.4KB, Terms of use)
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- Publisher copy:
- 10.1007/s00493-023-00061-4
Authors
- Publisher:
- Springer Nature
- Journal:
- Combinatorica More from this journal
- Volume:
- 44
- Issue:
- 1
- Pages:
- 37–62
- Publication date:
- 2023-09-25
- Acceptance date:
- 2023-08-17
- DOI:
- EISSN:
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1439-6912
- ISSN:
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0209-9683
- Language:
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English
- Keywords:
- Pubs id:
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1514084
- Local pid:
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pubs:1514084
- Deposit date:
-
2023-08-21
Terms of use
- Copyright holder:
- Girão et al
- Copyright date:
- 2023
- Rights statement:
- © 2023, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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