Bibliographic record
Abstract
Abstract The honeymoon Oberwolfach problem HOP asks the following question. Given newlywed couples at a conference and round tables of sizes , is it possible to arrange the participants at these tables for meals so that each participant sits next to their spouse at every meal and sits next to every other participant exactly once? A solution to HOP is a decomposition of , the complete graph with additional copies of a fixed 1‐factor , into 2‐factors, each consisting of disjoint ‐alternating cycles of lengths . It is also equivalent to a semi‐uniform 1‐factorization of of type ; that is, a 1‐factorization such that for all , the 2‐factor consists of disjoint cycles of lengths . In this paper, we first introduce the honeymoon Oberwolfach problem and then present several results. Most notably, we completely solve the case with uniform cycle lengths, that is, HOP . In addition, we show that HOP has a solution in each of the following cases: ; is odd and ; as well as for all . We also show that HOP has a solution whenever is odd and the Oberwolfach problem with tables of sizes has a solution.
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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 | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.004 | 0.002 |
| Insufficient payload (model declined to judge) | 0.021 | 0.002 |
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".