The 3-Colour Ramsey Number of a 3-Uniform Berge Cycle
نویسندگان
چکیده
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 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 K (3) n .
منابع مشابه
The 3-color Ramsey number of a 3-uniform Berge-cycle
The asymptotics of 2-color Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs have been recently determined ([16], [17]). We address here the same problem for Berge-cycles and for 3 colors. Our main result is that the 3-color Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n 4 . The result is proved with the Regularity Lemma via the existence of a monochrom...
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 20 شماره
صفحات -
تاریخ انتشار 2011