Partitioning a graph into two isomorphic pieces
Bibliographic record
Abstract
Abstract A simple graph G has the neighbour‐closed‐co‐neighbour property, or ncc property, if for all vertices x of G , the subgraph induced by the set of neighbours of x is isomorphic to the subgraph induced by the set of non‐neighbours of x . We present characterizations of graphs with the ncc property via the existence of certain perfect matchings, and thereby prove that the ncc graphs can be recognized in polynomial time. Operations preserving the ncc property are discussed, and the graphs with the ncc property that are r ‐regular, where r ≤ 5, are classified. The graphs with the ncc property that are locally H , for certain graphs H are classified. Infinite graphs with the ncc property are discussed. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 1–14, 2003
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".