[xovjnqtf] Quadrilateral-free bipartite graphs

Any two-coloring of the edges of the complete bipartite graph K(5,5) will contain a quadrilateral (i.e., K(2,2) = C₄) of one color.  Any three-coloring of K(11,11) will contain a quadrilateral of one color. These are "quadrilateral" generalizations of the game of Sim, played on a hexagon and trying to avoid a triangle. The quadrilaterals will necessarily be bowties, but I think it's still more elegant than avoiding tetrahedra (K₄) on a plane as in the standard Ramsey problem. Also R(3,3,3)=17.

Wayne Goddard, Michael A. Henning, Ortrud R. Oellermann. Bipartite Ramsey Numbers and Zarankiewicz Numbers.