Geodesic
Choice-Perfect Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 231-242.

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Given a graph G = (V,E) and a set L_v of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring ϕ : V →⋃_v ∈ V L_v such that ϕ (v) ∈ L_v for all v ∈ V and ϕ(u) ϕ(v) for all uv ∈ E. If such a ϕ exists, G is said to be list colorable. The choice number of G is the smallest natural number k for which G is list colorable whenever each list contains at least k colors. In this note we initiate the study of graphs in which the choice number equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, respectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.
Keywords: graph coloring, list coloring, choice-perfect graph 
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Tuza, Zsolt. Choice-Perfect Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 231-242. http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a18/

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