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

R.A. Sitters

Research output: Book/ReportReportProfessional

### 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 Enschede Universiteit Twente 5 0169-2690 Published - 1998

### Publication series

Name Memorandum / Faculty of Mathematical Sciences Department of Applied Mathematics, University of Twente 1477 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.
Sitters, R.A. / A short proof of a conjecture on the Tr-choice number of even cycles. Enschede : Universiteit Twente, 1998. 5 p. (Memorandum / Faculty of Mathematical Sciences; 1477).
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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.",
keywords = "MSC-05C15, Graph colouring, Tr-choice number, even cycle, METIS-141277, choosability, EWI-3297, list colouring, IR-65666, choice number",
author = "R.A. Sitters",
note = "Memorandum Faculteit TW, nr 1477",
year = "1998",
language = "Undefined",
isbn = "0169-2690",
series = "Memorandum / Faculty of Mathematical Sciences",
publisher = "Universiteit Twente",
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Sitters, RA 1998, A short proof of a conjecture on the Tr-choice number of even cycles. Memorandum / Faculty of Mathematical Sciences, no. 1477, Universiteit Twente, Enschede.
Enschede : Universiteit Twente, 1998. 5 p. (Memorandum / Faculty of Mathematical Sciences; No. 1477).

Research output: Book/ReportReportProfessional

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 -

Sitters RA. A short proof of a conjecture on the Tr-choice number of even cycles. Enschede: Universiteit Twente, 1998. 5 p. (Memorandum / Faculty of Mathematical Sciences; 1477).