Rado Numbers and SAT Computations

Given a linear equation E, the k-color Rado number Rk(E) is the smallest integer n such that every k-coloring of {1,2,3,...,n} contains a monochromatic solution to E. The degree of regularity of E, denoted dor(E), is the largest value k such that Rk(E) is finite. In this article we present new theoretical and computational results about the Rado numbers R3(E) and the degree of regularity of three-variable equations E.