The 3-colour ramsey number of a 3-uniform berge cycle

Authors:
AndrÁs GyÁrfÁs;GÁbor n. SÁrkÖzy
Affiliations:
Computer and automation research institute, hungarian academy of sciences, budapest, po box 63, budapest, hungary, h-1518 (e-mail: gyarfas@sztaki.hu);Computer and automation research institute, hungarian academy of sciences, budapest, po box 63, budapest, hungary, h-1518 (e-mail: gyarfas@sztaki.hu) and computer science department, worcester pol ...
Venue:
Combinatorics, Probability and Computing
Year:
2011

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Abstract

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to $\frac{5n}{4}$. The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4n/5 vertices in the multicoloured 2-shadow graph induced by the colouring of Kn(3).