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Record W3023986409 · doi:10.1002/jgt.22478

Almost all 5‐regular graphs have a 3‐flow

2019· article· en· W3023986409 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 · 2019
Typearticle
Languageen
FieldMathematics
TopicLimits and Structures in Graph Theory
Canadian institutionsToronto Metropolitan University
FundersNatural Sciences and Engineering Research Council of CanadaCentre of Excellence for Electromaterials Science, Australian Research Council
KeywordsMathematicsCombinatoricsConjectureDiscrete mathematics1-planar graphGraphChordal graph

Abstract

fetched live from OpenAlex

Abstract Tutte conjectured in 1972 that every 4‐edge–connected graph has a nowhere‐zero 3‐flow. This has long been known to be equivalent to the conjecture that every 5‐regular 4‐edge–connected graph has an edge orientation in which every in‐degree is either 1 or 4. We show that the assertion of the conjecture holds asymptotically almost surely for random 5‐regular graphs. It follows that the conjecture holds for almost all 4‐edge–connected 5‐regular graphs.

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)0.000
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 score0.009
Threshold uncertainty score0.862

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.000

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 head0.019
GPT teacher head0.278
Teacher spread0.259 · 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