Bucic, M. and Kwan, M. and Pokrovskiy, Alexey and Sudakov, B. and Tran, T. and Wagner, A.Z. (2020) Nearly-linear monotone paths in edge-ordered graphs. Israel Journal of Mathematics 238 , pp. 663-685. ISSN 0021-2172.
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Abstract
How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n^2/3−o(1). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n^1−o(1).
Metadata
| Item Type: | Article |
|---|---|
| Additional Information: | The final publication is available at Springer via the link above. |
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 20 Jan 2020 13:23 |
| Last Modified: | 02 Aug 2023 17:56 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/30606 |
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