On Helly Hypergraphs with Variable Intersection Sizes.
Bibliographic record
Abstract
A hypergraphH is said to be p-Helly when every p-wise intersecting partial hypergraph H′ of H has nonempty total intersection. Such hypergraphs have been characterized by Berge and Duchet in 1975, and since then they have appeared in the literature in several contexts, especially for the case p = 2, in which they are referred simply as Helly hypergraphs. An interesting generalization of p-Helly hypergraphs due to Voloshin takes into account not only the number of intersecting sets, but also the intersection sizes: we say that a hypergraph H is (p, q, s)-Helly when every p-wise q-intersecting partial hypergraph H′ of H has total intersection of cardinality at least s. In this work we propose a characterization for (p, q, s)-Helly hypergraphs. This characterization leads to an efficient algorithm to recognize such hypergraphs when p and q are fixed parameters.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".