### 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) |
---|---|

Pages (from-to) | 309-334 |

Number of pages | 26 |

Journal | Journal of Graph Theory |

Volume | 74 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2013 |

### Fingerprint

### Keywords

- choosable
- equitable coloring
- list coloring
- maximum degree

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Journal of Graph Theory*,

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

**Equitable list coloring of graphs with bounded degree.** / Kierstead, Henry; Kostochka, A. V.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 74, no. 3, pp. 309-334. https://doi.org/10.1002/jgt.21710

}

TY - JOUR

T1 - Equitable list coloring of graphs with bounded degree

AU - Kierstead, Henry

AU - Kostochka, A. V.

PY - 2013/11

Y1 - 2013/11

N2 - 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.

AB - 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.

KW - choosable

KW - equitable coloring

KW - list coloring

KW - maximum degree

UR - http://www.scopus.com/inward/record.url?scp=84883547892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883547892&partnerID=8YFLogxK

U2 - 10.1002/jgt.21710

DO - 10.1002/jgt.21710

M3 - Article

AN - SCOPUS:84883547892

VL - 74

SP - 309

EP - 334

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -