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Record W2140423070 · doi:10.1002/jgt.20575

The chromatic Ramsey number of odd wheels

2011· article· en· W2140423070 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueJournal of Graph Theory · 2011
Typearticle
Languageen
FieldMathematics
TopicLimits and Structures in Graph Theory
Canadian institutionsRoyal Military College of Canada
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsCombinatoricsMathematicsChromatic scaleConjectureMonochromatic colorFriendship graphGraphWindmill graphCritical graphRamsey's theoremDiscrete mathematicsGraph powerLine graphPhysics

Abstract

fetched live from OpenAlex

Abstract We prove that the chromatic Ramsey number of every odd wheel W 2 k + 1 , k ⩾2 is 14. That is, for every odd wheel W 2 k + 1 , there exists a 14‐chromatic graph F such that when the edges of F are two‐coloured, there is a monochromatic copy of W 2 k + 1 in F , and no graph F with chromatic number 13 has the same property. We ask whether a natural extension of odd wheels to the family of generalized Mycielski graphs could help to prove the Burr–Erdős–Lovász conjecture on the minimum possible chromatic Ramsey number of an n ‐chromatic graph. © 2011 Wiley Periodicals, Inc. J Graph Theory 69:198‐205, 2012

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.003
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.034
Threshold uncertainty score0.541

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.040
GPT teacher head0.298
Teacher spread0.258 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it