Computational Evidence for a Conjecture in Graph Theory

We present computational evidence supporting the following conjecture: In any 2-coloring of the complete graph K_n, every Turán graph T(n,3) contains at least one monochromatic K_4, and the minimum number of monochromatic K_4 in any 2-coloring of K_18 is exactly 3.. An exhaustive search over 18 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.