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

Voir la notice de l'article dans European Digital Mathematics Library

Given a graph G = (V,E) and a set Lv 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 → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= 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.
Classification : 05C15, 05C17, 05C75
Mots-clés : graph coloring, list coloring, choice-perfect graph 
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Zsolt Tuza. Choice-Perfect Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 1, p. 231. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_1_267681/