# Choice-Perfect Graphs

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 1, page 231-242
- ISSN: 2083-5892

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topZsolt Tuza. "Choice-Perfect Graphs." Discussiones Mathematicae Graph Theory 33.1 (2013): 231-242. <http://eudml.org/doc/267681>.

@article{ZsoltTuza2013,

abstract = {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.},

author = {Zsolt Tuza},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph coloring; list coloring; choice-perfect graph},

language = {eng},

number = {1},

pages = {231-242},

title = {Choice-Perfect Graphs},

url = {http://eudml.org/doc/267681},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Zsolt Tuza

TI - Choice-Perfect Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 1

SP - 231

EP - 242

AB - 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.

LA - eng

KW - graph coloring; list coloring; choice-perfect graph

UR - http://eudml.org/doc/267681

ER -

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