On the (3,4)-Ramsey graphs without 9-cliques

Abstract

A set of $p$ verticles of a graph is called $p$-clique if any two of them are adjacent. The graph is called (3,4)-Ramsey graph if for every 2-colouring of the edges there exists a monochromatic 3-clique of the 1-th colour, or a monochromatic 4-clique of the 2-th colour; $\beta$ denotes the minimal natural number $n$ such there is (3,4)-Ramsey graph with $n$ verticles and without 9-cliques. In this paper it is proved that $\beta =14$