Multiple list colouring triangle-free planar graphs

TL;DR

This paper demonstrates that for every positive integer m, there exist triangle-free planar graphs that cannot be properly list-colored under certain parameters, highlighting limitations in list coloring.

Contribution

It introduces specific counterexamples showing the non-choosability of triangle-free planar graphs for particular list coloring parameters.

Findings

Existence of triangle-free planar graphs not (3m+⌈m/17⌉-1, m)-choosable for each m

Counterexamples challenge previous assumptions on list coloring bounds

Highlights limitations in list coloring of planar graphs

Abstract

This paper proves that for each positive integer $m$, there is a triangle-free planar graph $G$ which is not $(3m+ \lceil \frac m{17} \rceil-1, m)$-choosable.