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Abstract
A k-uniform tight cycle is a k-graph with a cyclic ordering of its vertices such that its edges are precisely the sets of k consecutive vertices in that ordering. A k-uniform tight path is a k-graph obtained by deleting a vertex from a k-uniform tight cycle. We prove that the Ramsey number for the 4-uniform tight cycle on 4n vertices is (5+o(1))n. This is asymptotically tight. This result also implies that the Ramsey number for the 4-uniform tight path on n vertices is (5/4+o(1))n.
Original language | English |
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Pages (from-to) | 361-387 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 39 |
Issue number | 1 |
Early online date | 6 Feb 2025 |
DOIs | |
Publication status | E-pub ahead of print - 6 Feb 2025 |
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Dive into the research topics of 'The Ramsey Number for 4-Uniform Tight Cycles'. Together they form a unique fingerprint.Projects
- 1 Finished
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Matchings and tilings in graphs
Lo, A. (Co-Investigator) & Treglown, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/03/21 → 29/02/24
Project: Research Councils