Year: 2026
Type: preprint
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 $χ(G)\,\leqslant\,1{,}118{,}430\,\text{had}(G)$.
Source: arXiv (Cornell University)
Author: Wood, David R.
Institution: Monash University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Australian Research Council
OpenAlex ID: W7221148525