Displaying similar documents to “Hales-Jewett's theorem without short cycles”

Rainbow Ramsey theory.

Jungić, Veselin, Nešetřil, Jaroslav, Radoičić, Radoš (2005)

Integers

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Rainbow Ramsey theorems for colorings establishing negative partition relations

András Hajnal (2008)

Fundamenta Mathematicae

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Given a function f, a subset of its domain is a rainbow subset for f if f is one-to-one on it. We start with an old Erdős problem: Assume f is a coloring of the pairs of ω₁ with three colors such that every subset A of ω₁ of size ω₁ contains a pair of each color. Does there exist a rainbow triangle? We investigate rainbow problems and results of this style for colorings of pairs establishing negative "square bracket" relations.