### Abstract

In this note we prove that the $T_r$-choice number of the cycle $C_{2n}$ is equal to the $T_r$-choice number of the path (tree) on $4n-1$ vertices, i.e. $T_r$-$ch(C_{2n}) = \left\lfloor(2r+2)(4n-2)/(4n-1)\right\rfloor + 1$. This solves a recent conjecture of Alon and Zaks.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Universiteit Twente |

Number of pages | 5 |

ISBN (Print) | 0169-2690 |

Publication status | Published - 1998 |

### Publication series

Name | Memorandum / Faculty of Mathematical Sciences |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1477 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C15
- Graph colouring
- Tr-choice number
- even cycle
- METIS-141277
- choosability
- EWI-3297
- list colouring
- IR-65666
- choice number

## Cite this

Sitters, R. A. (1998).

*A short proof of a conjecture on the Tr-choice number of even cycles*. (Memorandum / Faculty of Mathematical Sciences; No. 1477). Enschede: Universiteit Twente.