# 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