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.

Publication Date

2004

Comments

ISSN:0381-7032 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

Center for Advancing the Study of CyberInfrastructure

Campus

RIT – Main Campus

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