### Abstract

Original language | Undefined |
---|---|

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 |
---|---|

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

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

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*A short proof of a conjecture on the Tr-choice number of even cycles*. Memorandum / Faculty of Mathematical Sciences, no. 1477, Universiteit Twente, Enschede.

**A short proof of a conjecture on the Tr-choice number of even cycles.** / Sitters, R.A.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - A short proof of a conjecture on the Tr-choice number of even cycles

AU - Sitters, R.A.

N1 - Memorandum Faculteit TW, nr 1477

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - MSC-05C15

KW - Graph colouring

KW - Tr-choice number

KW - even cycle

KW - METIS-141277

KW - choosability

KW - EWI-3297

KW - list colouring

KW - IR-65666

KW - choice number

M3 - Report

SN - 0169-2690

T3 - Memorandum / Faculty of Mathematical Sciences

BT - A short proof of a conjecture on the Tr-choice number of even cycles

PB - Universiteit Twente

CY - Enschede

ER -