On the Classical Multicolor Ramsey Number R(3,3,3)
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In this paper, we are interested in the problem of evaluation of the classical multicolor Ramsey number i?(3,3,3). We first convert it successfully into a system of clauses of 3-literals each, i.e., a 3-SAT instance. We then describe the algebraic method of Greenwood and Gleason , which is based on the finite field Fl6, that constructs a monochromatic triangle-free edge-coloring with three colors of the Ramsey graph Kl6 associated with the number i?(3,3,3). We propose a simple and new coloring method, completely dif¬ferent from that of Greenwood and Gleason, which colors the edges of the Ramsey graph Ku with three colors without any monochromatic triangle.