Abstract

Abstract A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g with u, v ∈ e, v, w ∈ f , w, u ∈ g and {u, v, w} ∩ e ∩ f ∩ g = ∅. Johansson We provide a common generalization of both these results for rank 3 hypergraphs (edges have size 2 or 3). Our result removes the linear restriction from As an application, we prove that if C 3 is the collection of 3-uniform triangles, then the Ramsey number R(C 3 , K 3 t ) satisfies for some positive constants a and b. The upper bound makes progress towards the recent conjecture of Kostochka, the second author, and Verstraëte