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 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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".