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In 1973 P. Erd\H{o}s and L. Lov\'asz noticed that any hypergraph whose edgesare pairwise intersecting has chromatic number 2 or 3. In the first case, suchhypergraph may have any number of edges. However, Erd\H{o}s and Lov\'asz provedthat in the second case, the number of edges is bounded from above. Forexample, if a hypergraph is $ n $-uniform, has pairwise intersecting edges, andhas chromatic number 3, then the number of its edges does not exceed $ n^n $.Recently D.D. Cherkashin improved this bound (see \cite{Ch}). In this paper, wefurther improve it in the case when the number of vertices of an $n$-uniformhypergraph is bounded from above by $ n^m $ with some $ m = m(n) $.

About dependence of the number of edges and vertices in hypergraph clique with chromatic number 3