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The Linear List Hadwiger Conjecture

Theorem 1.1: there is an absolute integer $C\ge1$ such that every finite nonempty simple graph satisfies $\chi_\ell(G)\le C\,h(G)$ ; Corollary 1.2 gives the ordinary linear Hadwiger bound $\chi(G)\le C\,h(G)$ . The constant is not computed or optimised and must be at least $2$ by Steiner's examples. The proof shows $K_t$ -minor-free graphs on at most $t^{11/10}$ vertices are $Lt$ -choosable and then lifts this to all orders through Postle-style separability and a three-district recursion. It does not give $C$ close to $1$ or $2$ .

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Linear List Hadwiger Conjecture · Linear List Hadwiger conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
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Unreleased internal OpenAI model
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Evidence vector

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Named evidence

VibeMathed record: The Linear List Hadwiger Conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, introduction, Theorem 1.1 and the INPUTS.md file, read against Kawarabayashi-Mohar Conjecture 1.3 as cited. The proof was not refereed. INPUTS.md lists three results used without proof: the Reed-Seymour fractional bound, a connectivity-extraction theorem (Delcourt-Postle, credited to Girao-Narayanan) and a terminal-linkage theorem (Delcourt-Postle, after Bollobas-Thomason), plus LP duality. The manuscript is dated 23 September 2026 but cites work posted 1 October 2026, so the text was revised after its date. Lean-checked on the release's own Comparator challenge ListHadwiger (OAI.LinearListHadwiger.main_theorem) together with its solution module, both present at the pinned commit; the challenge is not listed in the release's formalization catalogue, the statement was read here but not independently audited, and the development was not rebuilt here.

Source ↗

A linear list-coloring bound in terms of the Hadwiger number

paper · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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The Furedi-Gyarfas-Simonyi Sharp Connected-Matching Conjecture

witness · pending

paper link supplied by the VibeMathed registry.

Source ↗

Kawarabayashi-Mohar 2007, JCTB 97

specialist registry · pending

problem-record link supplied by the VibeMathed registry.