منابع مشابه
New Lower Bounds for Some Multicolored Ramsey Numbers
In this article we use two different methods to find new lower bounds for some multicolored Ramsey numbers. In the first part we use the finite field method used by Greenwood and Gleason [GG] to show that R(5, 5, 5) ≥ 242 and R(6, 6, 6) ≥ 692. In the second part we extend Fan Chung’s result in [C] to show that, R(3, 3, 3, k1, k2, . . . , kr) ≥ 3R(3, 3, k1, k2, . . . , kr) + R(k1, k2, . . . , kr...
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The Ramsey number rk(s, n) is the minimum N such that for every red-blue coloring of the k-tuples of {1, . . . , N}, there are s integers such that every k-tuple among them is red, or n integers such that every k-tuple among them is blue. We prove the following new lower bounds for 4-uniform hypergraph Ramsey numbers: r4(5, n) > 2 n log n and r4(6, n) > 2 2 1/5 , where c is an absolute positive...
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For graphs G1, G2, · · · , Gm, the Ramsey number R(G1, G2, · · · , Gm) is defined to be the smallest integer n such that anym-coloring of the edges of the complete graphKn must include a monochromatic Gi in color i, for some i. In this note we establish several lower and upper bounds for some Ramsey numbers involving quadrilateral C4, including R(C4,K9) ≤ 32, 19 ≤ R(C4, C4,K4) ≤ 22, 31 ≤ R(C4, ...
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Article history: Received 4 April 2009 Available online 2 February 2010
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Xiaodong Xu, Guangxi Academy of Sciences, Nanning, China Zehui Shao, Huazhong University of Science and Technology, Wuhan, China Stanis law Radziszowski∗, Rochester Institute of Technology, NY, USA For graphs G1, G2, · · · , Gm, the Ramsey number R(G1, G2, · · · , Gm) is defined to be the smallest integer n such that any m-coloring of the edges of the complete graph Kn must include a monochroma...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1972
ISSN: 0012-365X
DOI: 10.1016/0012-365x(72)90009-x