On the minisymposium problem
Bibliographic record
Abstract
The generalized Oberwolfach problem asks for a factorization of the complete graph Kv into prescribed 2-factors and at most a 1-factor. When all 2-factors are pairwise isomorphic and v is odd, we have the classic Oberwolfach problem, which was originally stated as a seating problem: given v attendees at a conference with t circular tables such that the ith table seats ai people and ∑t{i=1} ai = v, find a seating arrangement over the (v-1)/2 days of the conference, so that every person sits next to each other person exactly once. In this paper we introduce the related minisymposium problem, which requires a solution to the generalized Oberwolfach problem on v vertices that contains a subsystem on m vertices. That is, the decomposition restricted to the required m vertices is a solution to the generalized Oberwolfach problem on m vertices. In the seating context above, the larger conference contains a minisymposium of m participants, and we also require that pairs of these m participants be seated next to each other for ⌊(m−1)/2⌋ of the days. When the cycles are as long as possible, i.e. v, m and v − m, a flexible method of Hilton and Johnson provides a solution. We use this result to provide further solutions when v ≡ m ≡ 2 (mod 4) and all cycle lengths are even. In addition, we provide extensive results in the case where all cycle lengths are equal to k, solving all cases when m ∣ v, except possibly when k is odd and v is even.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.003 | 0.012 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.028 | 0.004 |
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".