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PreprintCC0arXiv

The List Total Colouring Conjecture is False

  • Jonathan A. Noel
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Abstract

We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin--Kostochka--Woodall, Juvan--Mohar--Škrekovski and Hilton--Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.

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Cite

BibTeXRIS
BibTeX
@misc{noel2026list,
  title = {{The List Total Colouring Conjecture is False}},
  author = {Jonathan A. Noel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.38417},
  eprint = {2609.38417},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38417},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - The List Total Colouring Conjecture is False
AU  - Jonathan A. Noel
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.38417
UR  - https://arxiv.org/abs/2609.38417
AB  - We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin--Kostochka--Woodall, Juvan--Mohar--Škrekovski and Hilton--Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.
ER  -