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 chi denotes the usual chromatic number of G, we are interested in which kind of G is chi-choosable. This question contains a famous conjecture, which states that every line-graph is chi-choosable. We present some other classes of graphs that are chi-choosable; all these classes are related to claw-free graphs. (C) 1998 John Wiley & Sons, Inc.