List coloring in the absence of two subgraphs

A list assignment of a graph G=(V,E) is a function L that assigns a list L(u) of so-called admissible colors to each u∈V. The List Coloring problem is that of testing whether a given graph G=(V,E) has a coloring c that respects a given list assignment L, i.e., whether G has a mapping c:V→{1,2,…} such that (i) c(u)≠c(v) whenever uv∈E and (ii) c(u)∈L(u) for all u∈V. If a graph G has no induced subgraph isomorphic to some graph of a pair {H1,H2}, then G is called (H1,H2)-free. We completely characterize the complexity of List Coloring for (H1,H2)-free graphs.