Helly's theorem says that, if every d+1 elements of a given finite set of convex objects in Rd have a common point, there is a point common to all of the objects in the set. I...
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n 2ck contains a K4 whose edges receive at most two colors. Th...