Bibliographic record
Abstract
A graph G is bisectable if its edges can be colored by two colors so that the resulting monochromatic subgraphs are isomorphic. We show that any infinite tree of maximum degree Δ with infinitely many vertices of degree at least Δ −1 is bisectable as is any infinite tree of maximum degree Δ ≤ 4. Further, it is proved that every infinite tree T of finite maximum degree contains a finite subset E of its edges so that the graph T − E is bisectable. To measure how “far” a graph G is from being bisectable, we define c(G) to be the smallest number k > 1 so that there is a coloring of the edges of G by k colors with the property that any two monochromatic subgraphs are isomorphic. An upper bound on c(G), which is in a sense best possible, is presented. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 113–127, 2000
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.003 | 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".