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.
Department, Program, or Center
Center for Advancing the Study of CyberInfrastructure
Ars Combinatoria LXXIII (2004) 205-214
RIT – Main Campus