A 4-choosable graph that is not (8 : 2)-choosable

Zdeněk Dvořák (1) , Xiaolan Hu (2, 3) , Jean-Sébastien Sereni (4)

1 Center of Excellence — Institute for Theoretical Computer Science
2 School of Mathematics and Statistics [Wuhan University]
3 Hubei Key Laboratory of Mathematical Sciences
4 CNRS - Centre National de la Recherche Scientifique

In 1980, Erdős, Rubin and Taylor asked whether for all positive integers a, b, and m, every (a : b)-choosable graph is also (am : bm)-choosable. We provide a negative answer by exhibiting a 4-choosable graph that is not (8 : 2)-choosable.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Zdeněk Dvořák, Xiaolan Hu, Jean-Sébastien Sereni. A 4-choosable graph that is not (8 : 2)-choosable. Advances in Combinatorics, 2019, 1, ⟨10.19086/aic.10811⟩. ⟨hal-01812138v2⟩