Rainbow Turan numbers of matchings and forests of hyperstars in uniform hypergraphs

A hypergraph H is properly edge-colored if for every vertex v in H, all the edges incident to v have distinct colors. A rainbow hypergraph is an edge-colored hypergraph with all edges colored differently. For a fixed r-uniform hypergraph F, the maximum number of edges in a properly edge-colored r-uniform hypergraph on n vertices without a rainbow copy of F is called the rainbow Turan number of F, denoted by ex*(n, r, F). In this paper, we determine ex*(n, 3, F) when F is a matching of size s + 1 for all n > 6.1s. Furthermore, we determine ex*(n, r, F) when F is a forest of hyperstars for sufficiently large n. Here, a hyperstar is an r-uniform hypergraph with all edges having at least one vertex in common.(c) 2023 Published by Elsevier B.V.