A Note on Edge Coloring of Linear Hypergraphs

A k-edge coloring of a hypergraph H is a coloring of the edges of H with k colors such that any two intersecting edges receive distinct colors. The Erdos-Faber-Lovasz conjecture states that every loopless linear hypergraph with n vertices has an n-edge coloring. In 2021,Kang, Kelly, K¨uhn, Methuku and Osthus confirmed the conjecture for sufficiently large n. In this paper, the conjecture is verified for collision-weak hypergraphs. This result strictly extends two related ones of Bretto, Faisant and Hennecart in 2020.