English

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

Combinatorics 2019-10-28 v2

Abstract

In 1980, Erd\H{o}s, Rubin and Taylor asked whether for all positive integers aa, bb, and mm, every (a:b)(a:b)-choosable graph is also (am:bm)(am:bm)-choosable. We provide a negative answer by exhibiting a 44-choosable graph that is not (8:2)(8:2)-choosable.

Cite

@article{arxiv.1806.03880,
  title  = {A $4$-choosable graph that is not $(8:2)$-choosable},
  author = {Zdeněk Dvořák and Xiaolan Hu and Jean-Sébastien Sereni},
  journal= {arXiv preprint arXiv:1806.03880},
  year   = {2019}
}
R2 v1 2026-06-23T02:25:34.269Z