The asymptotic behavior of the correspondence chromatic number

L coloring is an important generalization of ordinary graph coloring, introduced independently by Vizing [6] and Erdős, Rubin, and Taylor [4]. It is defined as follows. Let G be a graph and suppose that for each vertex v ∈ V (G), a set of available colors L(v), called the list of v, is specified. A proper coloring c of G is an L-coloring if c(v) ∈ L(v) for all v ∈ V (G). G is said to be L-colorable if it admits an L-coloring; G is k-list-colorable (or k-choosable) if it is L-colorable whenever |L(v)| ≥ k for all v ∈ V (G). The least number k such that G is k-choosable is called the list chromatic number (or the choosability) of G and is denoted by χ`(G) (or ch(G)).