Gallai-Ramsey numbers for 3-uniform rainbow Berge triangles and monochromatic linear paths or cycles

Given two non-empty t-uniform hypergraphs G((t)), H-(t) and a positive integer k, the hypergraph Gallai-Ramsey number gr(k) (G((t)) : H-(t)) is defined as the minimum positive integer N such that for all n >= N, every k-hyperedge-coloring of t-uniform complete hypergraph K-n((t)) contains either a rainbow subhypergraph G((t)) or a monochromatic subhypergraph H-(t). A k-hyperedge-coloring of a hypergraph is exact if all colors are used at least once. In this paper, we get the exact values of hypergraph Gallai-Ramsey numbers for rainbow 3-uniform Berge triangles and monochromatic 3-uniform linear paths or cycles under exact k-hyperedge-coloring.(c) 2023 Elsevier B.V. All rights reserved.