Comparing list-color functions of uniform hypergraphs with their chromatic polynomials (II)

Abstract

For any r-uniform hypergraph H with m (≥2) edges, let P(H,k) and Pl(H,k) be the chromatic polynomial and the list-color function of H respectively, and let ρ(H) denote the minimum value of |e∖e′| among all pairs of distinct edges e,e′ in H. We will show that if r≥3, ρ(H)≥2 and m≥ρ(H)32+1, then Pl(H,k)=P(H,k) holds for all integers k≥2.4(m−1)ρ(H)log⁡(m−1).