The Ramsey number of Fano plane versus tight path

The hypergraph Ramsey number of two 3-uniform hypergraphs G and H, de- noted by R(G,H), is the least integer N such that every red-blue edge-coloring of the complete 3-uniform hypergraph on N vertices contains a red copy of G or a blue copy of H. The Fano plane F is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that R(H, F) ≥ 2(v(H) − 1) + 1. Hypergraphs H for which the equality holds are called F-good. Conlon asked to determine all H that are F-good. In this short paper we make progress on this problem and prove that the tight path of length n is F-good.