Asymptotics of the list-chromatic index for multigraphs

The list-chromatic index, X′₁(G) of a multigraph G is the least t such that if S(A) is a set of size t for each A ∈ E := E(G), then there exists a proper coloring σ of G with σ(A) ∈ S(A) for each A ∈ E. The list-chromatic index is bounded below by the ordinary chromatic index, X′(G), which in turn is at least the fractional chromatic index, X′*(G). In previous work we showed that the chromatic and fractional chromatic indices are asymptotically the same; here we extend this to the list-chromatic index: X′₁(G) ̃ X′*(G) as X′₁(G) → ∞. The proof uses sampling from "hard-core" distributions on the set of matchings of a multigraph to go from fractional to list colorings.