The <i>k</i>-conversion number of regular graphs
Bibliographic record
Abstract
Given a graph and a set an irreversible k -threshold conversion process on G is an iterative process wherein, for each St is obtained from by adjoining all vertices that have at least k neighbors in We call the set S0 the seed set of the process, and refer to S0 as an irreversible k-threshold conversion set, or a k-conversion set, of G if for some The k-conversion number is the size of a minimum k-conversion set of G. A set is a decycling set, or feedback vertex set, if and only if is acyclic. It is known that k-conversion sets in -regular graphs coincide with decycling sets. We characterize k-regular graphs having a k-conversion set of size k, discuss properties of -regular graphs having a k-conversion set of size k, and obtain a lower bound for for -regular graphs. We present classes of cubic graphs that attain the bound for and others that exceed it—for example, we construct classes of 3-connected cubic graphs Hm of arbitrary girth that exceed the lower bound for by at least m.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".