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

R.A. Sitters

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

R.A. Sitters

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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.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of 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

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title = "A short proof of a conjecture on the Tr-choice number of even cycles",

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\}) = \textbackslash{}left\textbackslash{}lfloor(2r+2)(4n-2)/(4n-1)\textbackslash{}right\textbackslash{}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",

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series = "Memorandum / Faculty of Mathematical Sciences",

publisher = "University of Twente",

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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

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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 - University of Twente

CY - Enschede

ER -