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PreprintCC BY-NC-SA 4.0arXiv

Tweaking the constant in the Linear Hadwiger Theorem

  • David R. Wood
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Abstract

Norin and Steiner recently proved the Linear Hadwiger Conjecture. That is, there is an absolute constant C such that every graph G satisfies χ(G)leqslant C had(G), where χ(G) is the chromatic number and had(G) is the Hadwiger number of G. They estimate that their proof gives a non-optimised constant C of order 10100. This paper uses AI assistance to optimise their argument, and shows that every graph G satisfies χ(G) leqslant 1,118,430 had(G).

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Cite

BibTeXRIS
BibTeX
@misc{wood2026tweaking,
  title = {{Tweaking the constant in the Linear Hadwiger Theorem}},
  author = {David R. Wood},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10831},
  eprint = {2610.10831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10831},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Tweaking the constant in the Linear Hadwiger Theorem
AU  - David R. Wood
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.10831
UR  - https://arxiv.org/abs/2610.10831
AB  - Norin and Steiner recently proved the Linear Hadwiger Conjecture. That is, there is an absolute constant C such that every graph G satisfies χ(G)leqslant C had(G), where χ(G) is the chromatic number and had(G) is the Hadwiger number of G. They estimate that their proof gives a non-optimised constant C of order 10^100. This paper uses AI assistance to optimise their argument, and shows that every graph G satisfies χ(G) leqslant 1,118,430 had(G).
ER  -