Eulerian $k$-dominating reconfiguration graphs
Why this work is in the frame
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Bibliographic record
Abstract
For a graph $G$, the vertices of the $k$-dominating graph, denoted $\mathcal{D}_k(G)$, correspond to the dominating sets of $G$ with cardinality at most $k$. Two vertices of $\mathcal{D}_k(G)$ are adjacent if and only if the corresponding dominating sets in $G$ can be obtained from one other by adding or removing a single vertex of $G$. Since $\mathcal{D}_k(G)$ is not necessarily connected when $k < |V(G)|$, much research has focused on conditions under which $\mathcal{D}_k(G)$ is connected and recent work has explored the existence of Hamilton paths in the $k$-dominating graph. We consider the complementary problem of determining the conditions under which the $k$-dominating graph is Eulerian. In the case where $k = |V(G)|$, we characterize those graphs $G$ for which $\mathcal{D}_k(G)$ is Eulerian. In the case where $k$ is restricted, we determine for a number of graph classes, the conditions under which the $k$-dominating graph is Eulerian. Comment: 13 pages, 5 figures
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| 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 it