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The Partial List Colouring Conjecture is False
Abstract
We exhibit a graph G with $14$ vertices and list chromatic number equal to $3$ such that there is a $2$-list assignment L of G such that at most $9$ vertices of G can be properly coloured from L. This disproves the Partial List Colouring Conjecture of Albertson, Grossman and Haas. This counterexample was discovered and fully verified by ChatGPT 6 Astra Ultra after some persistent prompting, but almost no mathematical input, from the author.
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BibTeX
@misc{noel2026partial,
title = {{The Partial List Colouring Conjecture is False}},
author = {Jonathan A. Noel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23291},
eprint = {2609.23291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23291},
}
RIS
TY - UNPB
TI - The Partial List Colouring Conjecture is False
AU - Jonathan A. Noel
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23291
UR - https://arxiv.org/abs/2609.23291
AB - We exhibit a graph G with $14$ vertices and list chromatic number equal to $3$ such that there is a $2$-list assignment L of G such that at most $9$ vertices of G can be properly coloured from L. This disproves the Partial List Colouring Conjecture of Albertson, Grossman and Haas. This counterexample was discovered and fully verified by ChatGPT 6 Astra Ultra after some persistent prompting, but almost no mathematical input, from the author.
ER -