What forms do interesting conjectures have in graph theory?
Bibliographic record
Abstract
Conjectures in graph theory have multiple forms and involve graph invariants, graph classes, subgraphs, minors and other concepts in premisses and/or conclusions.Various abstract criteria have been proposed in order to find interesting ones with computer-aided or automated systems for conjecturemaking.Beginning with the observation that famous theorems (and others) have first been conjectures, if only in the minds of those who obtained them, we review forms that they take.We also give examples of conjectures of such forms obtained with the help of, or by, computers when it is the case.It appears that many forms are unexplored and so computer-assisted and automated conjecture-making in graph theory, despite many successes, is pretty much at its beginning.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.007 |
| Scholarly communication | 0.008 | 0.022 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.039 | 0.007 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".