### Abstract

A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring of G such that every color class has at most âŒ̂|G|/kâŒ‰ vertices. We prove results toward the conjecture that every graph with maximum degree at most r is equitably (r+1)-choosable. In particular, we confirm the conjecture for r≤7 and show that every graph with maximum degree at most r and at least r ^{3} vertices is equitably (r+2)-choosable. Our proofs yield polynomial algorithms for corresponding equitable list colorings.

Original language | English (US) |
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Pages (from-to) | 309-334 |

Number of pages | 26 |

Journal | Journal of Graph Theory |

Volume | 74 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2013 |

### Keywords

- choosable
- equitable coloring
- list coloring
- maximum degree

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Kierstead, H. A., & Kostochka, A. V. (2013). Equitable list coloring of graphs with bounded degree.

*Journal of Graph Theory*,*74*(3), 309-334. https://doi.org/10.1002/jgt.21710