Book Ramsey Numbers and Quasi-randomness
نویسندگان
چکیده
A set of n triangles sharing a common edge is called a book with n pages and is denoted by Bn. It is known that the Ramsey number r (Bn) satisfies r (Bn) = (4 + o (1))n. We show that every red-blue edge coloring of Kb(4−ε)nc with no monochromatic Bn exhibits quasi-random properties when ε tends to 0. This implies that there is a constant c > 0 such that for every red-blue edge coloring of Kr(Bn) there is a monochromatic Bn inducing at least ⌊ cn2 ⌋ edges of its own color. As an application we find the Ramsey number for a class of graphs.
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