The Ramsey Number for 4-Uniform Tight Cycles

Allan Lo; Vincent Pfenninger

doi:10.48550/arXiv.2111.05276

The Ramsey Number for 4-Uniform Tight Cycles

Allan Lo
, Vincent Pfenninger^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	361-387
Journal	SIAM Journal on Discrete Mathematics
Volume	39
Issue number	1
Early online date	6 Feb 2025
DOIs	https://doi.org/10.48550/arXiv.2111.05276 https://doi.org/10.1137/21M1458089
Publication status	Published - Mar 2025

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10.48550/arXiv.2111.05276Licence: None: All rights reserved
10.1137/21M1458089Licence: None: All rights reserved

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

Cite this

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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. ",

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AB - 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.

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The Ramsey Number for 4-Uniform Tight Cycles

Abstract

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Matchings and tilings in graphs

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