Choice-Perfect Graphs

Zsolt Tuza

Discussiones Mathematicae Graph Theory (2013)

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

Abstract

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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.

How to cite

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Zsolt 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 -

References

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