Not evaluated
Coloring and independence in graphs with forbidden subgraphs (family 184)
The gist
On October 6, 2026, OpenAI released two manuscripts on correspondence colouring and on a logarithmic independence bound, for graphs that exclude a clique.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-184-coloring-independence-graphs-forbidden-r1
@misc{discoveria-oai-fam-184-coloring-independence-graphs-forbidden-r1,
author = {{DiscoverIA}},
title = {Coloring and independence in graphs with forbidden subgraphs (family 184)},
howpublished = {DiscoverIA registry, entry oai-fam-184-coloring-independence-graphs-forbidden},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-184-coloring-independence-graphs-forbidden#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscripts held, they would bring results on graphs from which a clique is excluded (a group of vertices all joined to one another). One concerns correspondence colouring (a variant of graph colouring). The other concerns a logarithmic independence bound, that is, the size of sets of vertices with no edge between them.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone: a single file for a family that has two manuscripts. The repository marks its review “unchecked”, and no third-party verification is recorded. The manuscripts come from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 184.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Correspondence-Coloring…link only, reading not recorded
- Repositorygithub.com · A-Logarithmic…link only, reading not recorded
- Lean proofgithub.com · 184.mdpage read word for word
- Lean proofgithub.com · CliqueFreeLog.leanlink only, reading not recorded
Method
In the openai/math release, family 184 has two manuscripts, filed under the section “Combinatorics” of overview.tex; history.md reports no revision. “Correspondence coloring graphs with a forbidden clique” is dated October 5, 2026, “A logarithmic independence bound for clique-free graphs” September 25, 2026. OpenAI adds a Lean Comparator file, lean/ComparatorChallenges/CliqueFreeLog.lean (1 statement), described in lean/docs/184.md. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Combinatorics)
- In openai/math
- family 184, section “Combinatorics”, 2 manuscripts dated Sep 25, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 5 : 1 read word for word, 4 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 178 of 372, by family number
- Not evaluated : The Erdős–Gallai cycle-decomposition conjecture (family 181)
- Not evaluated : Power savings for polynomial-difference-free sets (family 182)
- Not evaluated : Power savings for planar halving lines and k-sets (family 183)
- Not evaluated : Coloring and independence in graphs with forbidden subgraphs (family 184)
- Not evaluated : Counterexamples to infinite matroid intersection and packing/covering (family 185)
- Not evaluated : The Friedgut–Kalai graph and hypergraph threshold conjectures (family 186)
- Not evaluated : Snaky in 21 Maker moves (family 187)
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