Why this work is in the frame
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Bibliographic record
Abstract
Let G =( V , E ) be a simple graph of order n . We consider the problem of partitioning G into vertex-disjoint paths. We obtain the following new results: (i) For any positive integer k , if d G ( x )+ d G ( y ) = n - k -1 for every pair x , y of nonadjacent vertices in G , then G can be partitioned into k vertex-disjoint paths, unless G belongs to certain classes of extremal graphs which we characterize; (ii) For the case k =2, we strengthen our result by showing that for any two positive integers p 1 and p 2 satisfying n = p 1 + p 2 ,if d G ( x )+ d G ( y ) = n -3 for every pair x, y of nonadjacent vertices in G and G does not belong to classes of exceptional graphs we define, then G can be partitioned into two vertex-disjoint paths P 1 and P 2 of order p 1 and p 2 , respectively. These results are generalizations of some classical results of Dirac and Ore, and also lead to new sufficient conditions for the existence of a Hamilton path in a graph.
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.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it