Characterizing s-strongly chordal bipartite graphs
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Bibliographic record
Abstract
<p>The strongly chordal graph literature has recently expanded to include the sequentially smaller classes of <span class="math inline">\(s\)</span>-strongly chordal graphs for <span class="math inline">\(s = 1, 2, 3,\ldots\)</span> (and the limiting class of majorly chordal graphs). These stronger classes preserve — while simultaneously intensifying — the conventional chords-of-cycles inspiration of chordal graph theory. This leads to characterizing corresponding <span class="math inline">\(s\)</span>-strongly chordal bipartite graphs and majorly chordal bipartite graphs. Our new analysis does this by using chains of quadrangles, with each adjacent pair of quadrangles having a unique edge in common. This leads to constructive characterizations that exploit a somewhat unexpected resemblance to earlier characterizations of <span class="math inline">\(s\)</span>-strongly chordal graphs involving chains of triangles sharing common edges to characterize <span class="math inline">\(s\)</span>-strongly chordal tripartite (and, similarly, multipartite) graphs.</p>
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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 | 0.001 | 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 | 0.000 | 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 it