An Upper Bound for the Turلn Number t3(n, 4)

Let tr(n, r+1) denote the smallest integer m such that every r-uniform hypergraph on n vertices with m+1 edges must contain a complete graph on r+1 vertices. In this paper, we prove thatlimn→∞ t3(n, 4)(n3)⩽3+1712=0.593592… .