The Ramsey number of loose cycles versus cliques
نویسندگان
چکیده
منابع مشابه
Hypergraph Ramsey numbers: tight cycles versus cliques
For s ≥ 4, the 3-uniform tight cycle C s has vertex set corresponding to s distinct points on a circle and edge set given by the s cyclic intervals of three consecutive points. For fixed s ≥ 4 and s 6≡ 0 (mod 3) we prove that there are positive constants a and b with 2 < r(C s ,K 3 t ) < 2 bt log . The lower bound is obtained via a probabilistic construction. The upper bound for s > 5 is proved...
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The 3-uniform tight cycle C s has vertex set Zs and edge set {{i, i+ 1, i+ 2} : i ∈ Zs}. We prove that for every s 6≡ 0 (mod 3) and s ≥ 16 or s ∈ {8, 11, 14} there is a cs > 0 such that the 3-uniform hypergraph Ramsey number r(C s ,K n ) satisfies r(C s ,K n ) < 2cn . This answers in strong form a question of the author and Rödl who asked for an upper bound of the form 2n 1+ǫs for each fixed s ...
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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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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2018
ISSN: 0364-9024
DOI: 10.1002/jgt.22387