Open problems on graph coloring for special graph classes

Abstract

For a given graph G and integer k, the Coloring problem is that of testing whether G has a k-coloring, that is, whether there exists a vertex mapping c: V → {1, 2, …} such that c(u) ≠ c(v) for every edge uv ∈ E. We survey known results on the computational complexity of Coloring for graph classes that are hereditary or for which some graph parameter is bounded. We also consider coloring variants, such as precoloring extensions and list colorings and give some open problems in the area of on-line coloring.