A derivation of an affine plane of order 4 from a triangle-free 3-colored K16 Original Research Article

A variety of results connecting latin squares and graphs of different types, are known. In this paper a new relationship is given through the derivation of AG(2,4), the affine plane of order 4, from the 3-colored, triangle-free K16 constructed by Greenwood and Gleason in the proof that the classic Ramsey number R(3,3,3)=17. In the derivation each line of this affine plane is defined by a set of 4 vertices of the K16, which are mutually connected by edges of three colors so that each color defines one of three 1-factor of that K4.