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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2013_33_1_a18,
     author = {Tuza, Zsolt},
     title = {Choice-Perfect {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {231--242},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a18/}
}
TY  - JOUR
AU  - Tuza, Zsolt
TI  - Choice-Perfect Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2013
SP  - 231
EP  - 242
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a18/
LA  - en
ID  - DMGT_2013_33_1_a18
ER  - 
%0 Journal Article
%A Tuza, Zsolt
%T Choice-Perfect Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2013
%P 231-242
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a18/
%G en
%F DMGT_2013_33_1_a18
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/