Graphs whose choice number is equal to their chromatic number

A graph G is k-choosable if it admits a vertex-coloring whenever the colors allowed at each vertex are restricted to a list of length k. If χ denotes the usual chromatic number of G, we are interested in which kind of G is χ-choosable. This question contains a famous conjecture, which states that every line-graph is χ-choosable. We present some other classes of graphs that are χ-choosable; all these classes are related to claw-free graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 87–97, 1998