Ramsey numbers for triangles versus almost-complete graphs
We show that, in any coloring of the edges of K38 with two colors, there exists a triangle in the first color or a monochromatic K 10-e (K10 with one edge removed) in the second color, and hence we obtain a bound on the corresponding Ramsey number, R(K 3,K10-e) ≤ 38. The new lower bound of 37 for this number is established by a coloring of K36 avoiding triangles in the first color and K10-e in the second color. This improves by one the best previously known lower and upper bounds. We also give...[Show more]
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