منابع مشابه
Induced restricted Ramsey theorems for spaces
The induced restricted versions of the vector space Ramsey theorem and of the Graham-Rothschild parameter set theorem are proved.
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Let F , G and H be simple graphs. We say F → (G,H) if for every 2-coloring of the edges of F there exists a monochromatic G orH in F . The Ramsey number r(G,H) is defined as r(G,H) = min{|V (F )| : F → (G,H)}, while the restricted size Ramsey number r(G,H) is defined as r(G,H) = min{|E(F )| : F → (G,H), |V (F )| = r(G,H)}. In this paper we determine previously unknown restricted size Ramsey num...
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In earlier papers Sárközy studied the solvability of the equations a + b = cd, a ∈ A, b ∈ B, c ∈ C, d ∈ D, resp. ab + 1 = cd, a ∈ A, b ∈ B, c ∈ C, d ∈ D where A,B, C,D are “large” subsets of Fp. Later Gyarmati and Sárközy generalized and extended these problems by studying these equations and also other algebraic equations with restricted solution sets over finite fields. Here we will continue ...
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Let G and H be simple graphs. The Ramsey number r(G,H) for a pair of graphs G and H is the smallest number r such that any red-blue coloring of the edges of Kr contains a red subgraph G or a blue subgraph H . The size Ramsey number r̂(G,H) for a pair of graphs G and H is the smallest number r̂ such that there exists a graph F with size r̂ satisfying the property that any red-blue coloring of the e...
متن کاملMulticolor Ramsey Numbers and Restricted Turán Numbers for the Loose 3-Uniform Path of Length Three
Let P denote a 3-uniform hypergraph consisting of 7 vertices a, b, c, d, e, f, g and 3 edges {a, b, c}, {c, d, e}, and {e, f, g}. It is known that the r-colored Ramsey number for P is R(P ; r) = r + 6 for r = 2, 3, and that R(P ; r) 6 3r for all r > 3. The latter result follows by a standard application of the Turán number ex3(n;P ), which was determined to be ( n−1 2 ) in our previous work. We...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1975
ISSN: 0097-3165
DOI: 10.1016/0097-3165(75)90053-9