Clique‐width: Harnessing the power of atoms
Bibliographic record
Abstract
Abstract Many NP‐complete graph problems are polynomial‐time solvable on graph classes of bounded clique‐width. Several of these problems are polynomial‐time solvable on a hereditary graph class if they are so on the atoms (graphs with no clique cut‐set) of . Hence, we initiate a systematic study into boundedness of clique‐width of atoms of hereditary graph classes. A graph is ‐free if is not an induced subgraph of , and it is ‐free if it is both ‐free and ‐free. A class of ‐free graphs has bounded clique‐width if and only if its atoms have this property. This is no longer true for ‐free graphs, as evidenced by one known example. We prove the existence of another such pair and classify the boundedness of clique‐width on ‐free atoms for all but 18 cases.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".