Circular chromatic index of graphs of maximum degree 3
Bibliographic record
Abstract
Abstract This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′ c ( G ) ≤ 11/3 provided that G does not contain H 1 or H 2 as a subgraph, where H 1 and H 2 are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K 4 , respectively. As χ′ c ( H 1 ) = χ′ c ( H 2 ) = 4, our result implies that there is no graph G with 11/3 < χ′ c ( G ) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′ c ( G ) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.000 |
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.
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".