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.
@article{bwmeta1.element.doi-10_7151_dmgt_1660,
author = {Zsolt Tuza},
title = {Choice-Perfect Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {231-242},
zbl = {1293.05128},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1660}
}
Zsolt Tuza. Choice-Perfect Graphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 231-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1660/
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