Bibliographic record
Abstract
A brick is a $3$-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. A brick $G$ is near-bipartite if it has a pair of edges $α$ and $β$ such that $G-\{α,β\}$ is bipartite and matching covered; examples are $K_4$ and the triangular prism $\overline{C_6}$. The significance of near-bipartite bricks arises from the theory of ear decompositions of matching covered graphs. The object of this paper is to establish a generation procedure which is specific to the class of simple near-bipartite bricks. In particular, we prove that every simple near-bipartite brick $G$ has an edge $e$ so that the graph obtained from $G-e$ by contracting each edge that is incident with a vertex of degree two is also a simple near-bipartite brick, unless $G$ belongs to any of eight well-defined infinite families. This is a refinement of the brick generation theorem of Norine and Thomas (Generating Bricks, J. Combin. Theory Ser. B, 2007) which is appropriate for the restricted class of near-bipartite bricks. Earlier, the first author (Generating near-bipartite bricks, J. Graph Theory, 2019) proved a similar generation theorem for (not necessarily simple) near-bipartite bricks; we deduce our main result from this theorem. Our proof is based on the strategy of Carvalho, Lucchesi and Murty (2008) and uses several of their techniques and results. The results presented here also appear in the Ph.D. thesis of the first author.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".