Efficiently Enumerating Spanning Trees of <i>k</i> -Trees
Bibliographic record
Abstract
A spanning tree T of a connected graph G is an acyclic subgraph of G that connects all vertices of G with the minimum number of edges. Spanning tree enumeration is the problem of finding all distinct spanning trees of G and is a well-studied problem in graph theory with applications in various fields. In this paper, we propose an algorithm for enumerating spanning trees of k-trees that runs in [Formula: see text] time and takes [Formula: see text] space for a k-tree G having n vertices, m edges, and [Formula: see text] spanning trees. This is a substantial improvement in time complexity without increasing the space cost over the best spanning tree enumeration algorithm for general graphs which takes [Formula: see text] time and also requires [Formula: see text] space.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.004 | 0.001 |
| 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 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".