### Abstract

One of the authors has conjectured that every graph G with 2%(G) + 1 or fewer vertices is χ(G)-choosable. Motivated by this, we investigate the choice numbers of some complete k-partite graphs of order slightly larger than 2k, and settle the conjecture for some special cases. We also present several complete multi-partite graphs whose choice numbers are not equal to their chromatic numbers.

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

Pages (from-to) | 55-66 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 244 |

Issue number | 1-3 |

Publication status | Published - 2002 Feb 6 |

### Fingerprint

### Keywords

- Complete
- List coloring
- Multi-partite graphs

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*244*(1-3), 55-66.

**Choice number of some complete multi-partite graphs.** / Enomoto, Hikoe; Ohba, Kyoji; Ota, Katsuhiro; Sakamoto, Junko.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 244, no. 1-3, pp. 55-66.

}

TY - JOUR

T1 - Choice number of some complete multi-partite graphs

AU - Enomoto, Hikoe

AU - Ohba, Kyoji

AU - Ota, Katsuhiro

AU - Sakamoto, Junko

PY - 2002/2/6

Y1 - 2002/2/6

N2 - One of the authors has conjectured that every graph G with 2%(G) + 1 or fewer vertices is χ(G)-choosable. Motivated by this, we investigate the choice numbers of some complete k-partite graphs of order slightly larger than 2k, and settle the conjecture for some special cases. We also present several complete multi-partite graphs whose choice numbers are not equal to their chromatic numbers.

AB - One of the authors has conjectured that every graph G with 2%(G) + 1 or fewer vertices is χ(G)-choosable. Motivated by this, we investigate the choice numbers of some complete k-partite graphs of order slightly larger than 2k, and settle the conjecture for some special cases. We also present several complete multi-partite graphs whose choice numbers are not equal to their chromatic numbers.

KW - Complete

KW - List coloring

KW - Multi-partite graphs

UR - http://www.scopus.com/inward/record.url?scp=33750981870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750981870&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33750981870

VL - 244

SP - 55

EP - 66

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -