Lower bounds for hypergraph Ramsey numbers
نویسندگان
چکیده
منابع مشابه
New 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 کاملA note on lower bounds for hypergraph Ramsey numbers
We improve upon the lower bound for 3-colour hypergraph Ramsey numbers, showing, in the 3-uniform case, that r3(l, l, l) ≥ 2 c log log l . The old bound, due to Erdős and Hajnal, was r3(l, l, l) ≥ 2 2 log2 .
متن کاملHypergraph 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...
متن کاملOff-diagonal hypergraph Ramsey numbers
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...
متن کاملNew lower bounds for Ramsey numbers of graphs and hypergraphs
Let G be an r-uniform hypergraph. The multicolor Ramsey number rk(G) is the minimum n such that every k-coloring of the edges of the complete r-uniform hypergraph K n yields a monochromatic copy of G. Improving slightly upon results from [1], we prove that tk + 1 ≤ rk(K2,t+1) ≤ tk + k + 2, where the lower bound holds when t and k are both powers of a prime p. When t = 1, we improve the lower bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1995
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)00167-c