A Note on Edge Coloring of Linear Hypergraphs

Abstract:

      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 Erd\H{o}s-Faber-Lov\'asz 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.