The Ramsey Number for 4-Uniform Tight Cycles

Allan Lo, Vincent Pfenninger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)361-387
JournalSIAM Journal on Discrete Mathematics
Volume39
Issue number1
Early online date6 Feb 2025
DOIs
Publication statusE-pub ahead of print - 6 Feb 2025

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