Bibliographic record
Abstract
We consider a variant of the Cops and Robbers game where the robber can move t edges at a time, and show that in this variant, the cop number of a d -regular graph with girth larger than 2 t +2 is Ω( d t ). By the known upper bounds on the order of cages, this implies that the cop number of a connected n -vertex graph can be as large as Ω( n 2/3 ) if t ≥ 2, and Ω( n 4/5 ) if t ≥ 4. This improves the Ω( $n^{\frac{t-3}{t-2}}$ ) lower bound of Frieze, Krivelevich and Loh (Variations on cops and robbers, J. Graph Theory , to appear) when 2 ≤ t ≤ 6. We also conjecture a general upper bound O ( n t / t +1 ) for the cop number in this variant, generalizing Meyniel's conjecture.
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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 | 0.024 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.006 | 0.015 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.018 | 0.003 |
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".