### 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 →U_{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 num- ber equals the clique number or the chromatic number in every induced subgraph. We call them choice-ω-perfect and choice-χ-perfect graphs, re- spectively. The main result of the paper states that the square of every cycle is choice-χ-perfect.

Original language | English |
---|---|

Pages (from-to) | 231-242 |

Number of pages | 12 |

Journal | Discussiones Mathematicae - Graph Theory |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 24 2013 |

### Keywords

- Choice-perfect graph
- Graph coloring
- List coloring

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Choice-perfect graphs'. Together they form a unique fingerprint.

## Cite this

*Discussiones Mathematicae - Graph Theory*,

*33*(1), 231-242. https://doi.org/10.7151/dmgt.1660