On the Ramsey (3,4)-multiplicity

Abstract

Let $M_n(3,4)$ be the minimal sum of the 3-clique's and 4-anticlique's numbers in an arbitrary $n$-vertex graph. The asymptotic formula $M_n(3,4)~m(3,4) \Big( \begin{matrix} n\\3 \end{matrix}\Big)$ with $\frac{1}{30} \leq m(3,4) \leq \frac{1}{9}$ is proved