The <i>n</i>‐ordered graphs: A new graph class
Bibliographic record
Abstract
Abstract For a positive integer n , we introduce the new graph class of n ‐ordered graphs, which generalize partial n ‐trees. Several characterizations are given for the finite n ‐ordered graphs, including one via a combinatorial game. We introduce new countably infinite graphs R (n) , which we name the infinite random n ‐ordered graphs. The graphs R (n) play a crucial role in the theory of n ‐ordered graphs, and are inspired by recent research on the web graph and the infinite random graph. We characterize R (n) as a limit of a random process, and via an adjacency property and a certain folding operation. We prove that the induced subgraphs of R (n) are exactly the countable n ‐ordered graphs. We show that all countable groups embed in the automorphism group of R (n) . © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 204–218, 2009
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".