On K4′-graphs

Abstract

$G$ is called $K_4^{\prime }$-graph if for every 2-coloring of its edges there are monochromatic triangles with common edge. By $R^k(K_4^{\prime })$ we denote the minimum of vertex number of $K_4^{\prime }$-graphs with clique number $k$. The inequalities $R^5(K_4^{\prime })\le 29$ and $R^4(K_4^{\prime })\le 61$ are proved.