Tweaking the constant in the Linear Hadwiger Theorem

David R. Wood

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arXiv · 2610.10831

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 $χ(G)\leqslant C\,\text{had}(G)$, where $χ(G)$ is the chromatic number and $\text{had}(G)$ 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 $χ(G)\,\leqslant\,1{,}118{,}430\,\text{had}(G)$.

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David R. Wood. 2026-10-16. Tweaking the constant in the Linear Hadwiger Theorem. https://arxiv.org/abs/2610.10831

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