List coloring in the absence of two subgraphs

Abstract

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 {H 1, H2}, then G is called (H 1, H2)-free. We completely characterize the complexity of List Coloring for (H1, H2)-free graphs. © 2013 Springer-Verlag.