Sharp thresholds for hypergraph regressive Ramsey numbers
نویسندگان
چکیده
منابع مشابه
Sharp thresholds for hypergraph regressive Ramsey numbers
The f -regressive Ramsey number R f (d, n) is the minimum N such that every colouring of the d-tuples of an N -element set mapping each x1, . . . , xd to a colour ≤ f(x1) contains a min-homogeneous set of size n, where a set is called min-homogeneous if every two d-tuples from this set that have the same smallest element get the same colour. If f is the identity, then we are dealing with the st...
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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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We give an elementary proof of the fact that regressive Ramsey numbers are Ackermannian. This fact was first proved by Kanamori and McAloon with mathematical logic techniques. Nous vivons encore sous le règne de la logique, voilà, bien entendu, à quoi je voulais en venir. Mais les procédés logiques, de nos jours, ne s’appliquent plus qu’à la résolution de problèmes d’intérêt secondaire. [1, 192...
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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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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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2010.08.004