Disjoint clique cutsets in graphs without long holes
Bibliographic record
Abstract
Abstract A biclique cutset is a cutset that induces the disjoint union of two cliques. A hole is an induced cycle with at least five vertices. A graph is biclique separable if it has no holes and each induced subgraph that is not a clique contains a clique cutset or a biclique cutset. The class of biclique separable graphs contains several well‐studied graph classes, including triangulated graphs. We prove that for the class of biclique separable graphs, the recognition problem, the vertex coloring problem, and the clique problem can be solved efficiently. Our algorithms also yield a proof that biclique separable graphs are perfect. Our coloring algorithm is actually more general and can be applied to graphs that can be decomposed via a special type of biclique cutset. Our algorithms are based on structural results on biclique separable graphs developed in this paper. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 277–298, 2005
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.004 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".