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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 ofG, we are interested in which kind ofG isχ-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. c © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 87–97, 1998

Graphs whose choice number is equal to their chromatic number