The Ramsey Number of Loose Triangles and Quadrangles in Hypergraphs
نویسندگان
چکیده
منابع مشابه
The Ramsey Number of Loose Triangles and Quadrangles in Hypergraphs
Asymptotic values of hypergraph Ramsey numbers for loose cycles (and paths) were determined recently. Here we determine some of them exactly, for example the 2-color hypergraph Ramsey number of a k-uniform loose 3-cycle or 4-cycle: R(Ck 3 , Ck 3 ) = 3k − 2 and R(Ck 4 , Ck 4 ) = 4k − 3 (for k > 3). For more than 3 colors we could prove only that R(C3 3 , C3 3 , C3 3) = 8. Nevertheless, the r-col...
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Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n > ⌊ 5m 4 ⌋ , we show that R(P n,P m) = 2n + ⌊m + 1 2 ⌋ .
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The 2-color Ramsey number R(C3 n, C3 n) of a 3-uniform loose cycle Cn is asymptotic to 5n/4 as has been recently proved by Haxell, Luczak, Peng, Rödl, Ruciński, Simonovits and Skokan. Here we extend their result to the r-uniform case by showing that the corresponding Ramsey number is asymptotic to (2r−1)n 2r−2 . Partly as a tool, partly as a subject of its own, we also prove that for r ≥ 2, R(k...
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A k-matching in a hypergraph is a set of k edges such that no two of these edges intersect. The anti-Ramsey number of a k-matching in a complete s-uniform hypergraph H on n vertices, denoted by ar(n, s, k), is the smallest integer c such that in any coloring of the edges of H with exactly c colors, there is a k-matching whose edges have distinct colors. The Turán number, denoted by ex(n, s, k),...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2346