Triangles in a complete chromatic graph with three colors

Abstract

AbstractLet KN be the complete graph on N vertices, and assume that each edge is assigned precisly one of three possible colors. An old and difficult problem is to find the minimum number of monochromatic triangles as a function of N. We are not able to solve this problem, but we can give sharp bounds for certain combinations of the number of triangles of various kinds. These sharp bounds are related to the main problem, and may be of indepdendent interest