Ramsey numbers for triangles versus almost-complete graphs

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Title: Ramsey numbers for triangles versus almost-complete graphs
Author: McKay, Brendan; Piwakowski, Konrad; Radziszowski, Stanislaw
Abstract: We show that, in any coloring of the edges of K_38 with two colors, there exists a triangle in the first color or a monochromatic K_10-e (K_10 with one edge removed) in the second color, and hence we obtain a bound on the corresponding Ramsey number, R(K_3, K_10-e) <= 38. the new lower bound of 37 for this number is established by a coloring of K_36 avoiding triangles in the first color and K_10-e in the second color. This improves by one the vest previously known lower and upper bounds. we also give the bounds for the next Ramsey number of this type, 42 <= R(K_3, K_11-e) <= 47.
Record URI: http://hdl.handle.net/1850/8001
Date: 2004

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