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For given finite family of graphs G) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of G i colored with i, for some 1 ≤ i ≤ k. We give a lower bound for k−color Ramsey number R(C m , C m ,. .. , C m), where m ≥ 4 is even and C m is the cycle on… (More)

We prove the following theorems: (1) Suppose that f : 2 ω → 2 ω is a continuous function and X is a Sierpi´nski set. Then (A) for any strongly measure zero set Y , the image f [X + Y ] is an s 0-set, (B) f [X] is a perfectly meager set in the transitive sense. (2) Every strongly meager set is completely Ramsey null. This paper is a continuation of earlier… (More)

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