Journal article
Flashes and rainbows in tournaments
- Abstract:
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Colour the edges of the complete graph with vertex set {1,2,...,n} with an arbitrary number of colours. What is the smallest integer f (l,k) such that if n > f (l,k) then there must exist a monotone monochromatic path of length l or a monotone rainbow path of length k? Lefmann, Rödl, and Thomasconjectured in1992that f (l,k) = lk−1 and proved this for l ě (3k)2k. We prove the conjecture for l ě k3(logk)1+o(1) and establish the general upper bound f (l,k) ď k(logk)1+o(1) &middo...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Version of record, pdf, 298.2KB, Terms of use)
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- Publisher copy:
- 10.1007/s00493-024-00090-7
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Funding
Bibliographic Details
- Publisher:
- Springer
- Journal:
- Combinatorica More from this journal
- Volume:
- 44
- Issue:
- 3
- Pages:
- 675-690
- Publication date:
- 2024-04-04
- Acceptance date:
- 2024-02-01
- DOI:
- EISSN:
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1439-6912
- ISSN:
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0209-9683
Item Description
- Language:
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English
- Keywords:
- Pubs id:
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1611172
- Local pid:
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pubs:1611172
- Deposit date:
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2024-02-01
Terms of use
- Copyright holder:
- Girão et al
- Copyright date:
- 2024
- Rights statement:
- Copyright © 2024, 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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