Ramsey-Type Problem for an Almost Monochromatic $K_4$
نویسندگان
چکیده
منابع مشابه
Ramsey-type Problem for an Almost Monochromatic
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n ≥ 2ck contains a K4 whose edges receive at most two colors. This improves on a result of Kostochka and Mubayi, and is the first exponential bound for this problem.
متن کاملRamsey-Type Problem for an Almost Monochromatic K4
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n ≥ 2 ck contains a K4 whose edges receive at most two colors. This improves on a result of Kostochka and Mubayi, and is the first exponential bound for this problem.
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In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n ≥ 2 contains a K4 whose edges receive at most two colors. This improves on a result of Kostochka and Mubayi, and is the first exponential bound for this problem.
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Suppose that n > (log k), where c is a fixed positive constant. We prove that no matter how the edges of Kn are colored with k colors, there is a copy of K4 whose edges receive at most two colors. This improves the previous best bound of k k, where c′ is a fixed positive constant, which follows from results on classical Ramsey numbers.
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For every fixed integers r, s satisfying 2 ≤ r < s there exists some = (r, s) > 0 for which we construct explicitly an infinite family of graphs Hr,s,n, where Hr,s,n has n vertices, contains no clique on s vertices and every subset of at least n1− of its vertices contains a clique of size r. The constructions are based on spectral and geometric techniques, some properties of Finite Geometries a...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2009
ISSN: 0895-4801,1095-7146
DOI: 10.1137/070706628