The linear Hadwiger conjecture asserts that there is an absolute constant 
such that every finite graph 
satisfies
 |
where 
is the chromatic number and 
is the Hadwiger number.
Equivalently, every graph with no complete
graph 
as a graph minor can be colored with at most 
colors. Unlike the Hadwiger conjecture, this
permits a fixed constant factor rather than requiring 
.
Norin and Steiner (2026) reported a proof. Norin and Steiner (2026) state that ChatGPT Astra 6 developed the proof following
their research directions and feedback and that they take responsibility for the
mathematical correctness. The full Hadwiger conjecture
asserts 
.
Wood (2026) reported the explicit bound 
in the revised version of his paper.
Wood (2026) states that Claude Opus 5.5 optimized the proof and that GPT-6 performed
checks. The author reports understanding the high-level argument but not checking
every detail by hand. Wood (2026) reports a Lean formalization of the revised bound
using only the standard axioms.
