A lower bound for the Ramsey multiplicity of \(K_4\) (Q2713626)

For a graph \(G\), the Ramsey multiplicity \(R(G)\) is defined as the smallest number of monochromatic copies of \(G\) in any two-coloring of the edges of \(K_{r(G)}\), where \(r(G)\) is the Ramsey number of \(G\). It is shown that \(R(K_4)\geq 4\). In other words, there are at least four monochromatic copies of \(K_4\) in any two-coloring of the edges of \(K_{18}\). The best known upper bound is \(R(K_4)\leq 9\). The Ramsey multiplicity \(R(G)\) of all other graphs \(G\) with at most \(4\) vertices was determined already in the seventies.