Bibliographic record
Abstract
Abstract: A vertex k-ranking of a graph G is a function c: V (G) → {1,...,k} such that if c(u) = c(v),u,v ∈ V (G) then each path connecting vertices u and v contains a vertex w with c(w)> c(u). If each vertex v has a list of integers L(v) and for a vertex ranking c it holds c(v) ∈ L(v) for each v ∈ V (G) then c is called L-list k-ranking, where L = {L(v) : v ∈ V (G)}. In this paper we investigate both vertex and edge (vertex ranking of a line graph) list ranking problems. We prove that both problems are NP-complete for several classes of acyclic graphs, like full binary trees, trees with diameter at most 4 and comets. The problem of finding vertex (edge) L-list ranking is polynomially solvable for paths and trees with bounded number of nonleaves, which includes trees with diameter less than 4. 1
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.001 |
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".