منابع مشابه
Hypergraph Ramsey numbers
The Ramsey number rk(s, n) is the minimum N such that every red-blue coloring of the k-tuples of an N -element set contains either a red set of size s or a blue set of size n, where a set is called red (blue) if all k-tuples from this set are red (blue). In this paper we obtain new estimates for several basic hypergraph Ramsey problems. We give a new upper bound for rk(s, n) for k ≥ 3 and s fix...
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The Ramsey number rk(s, n) is the minimum N such that every red-blue coloring of the k-subsets of {1, . . . , N} contains a red set of size s or a blue set of size n, where a set is red (blue) if all of its k-subsets are red (blue). A k-uniform tight path of size s, denoted by Ps, is a set of s vertices v1 < · · · < vs in Z, and all s−k+1 edges of the form {vj , vj+1, . . . , vj+k−1}. Let rk(Ps...
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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...
متن کاملNew lower bounds for hypergraph Ramsey numbers
The Ramsey number rk(s, n) is the minimum N such that for every red-blue coloring of the k-tuples of {1, . . . , N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We prove the following new lower bounds for 4-uniform hypergraph Ramsey numbers: r4(5, n) > 2 n log n and r4(6, n) > 2 2 1/5 , where c is an absolute positive...
متن کاملHypergraph Packing and Sparse Bipartite Ramsey Numbers
We prove that there exists a constant c such that, for any integer ∆, the Ramsey number of a bipartite graph on n vertices with maximum degree ∆ is less than 2n. A probabilistic argument due to Graham, Rödl and Ruciński implies that this result is essentially sharp, up to the constant c in the exponent. Our proof hinges upon a quantitative form of a hypergraph packing result of Rödl, Ruciński a...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2010
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-09-00645-6