Fractionally total colouring most graphs
Bibliographic record
Abstract
A total colouring is the assignment of a colour to each vertex and edge of a graph such that no adjacent vertices or incident edges receive the same colour and no edge receives the same colour as one of its endpoints.If we formulate the problem of finding the total chromatic number as an integer program, we can consider the fractional relaxation known as fractional total colouring.In this thesis we present an algorithm for computing the fractional total chromatic number of a graph, which runs in polynomial time on average.We also present an algorithm that asymptotically almost surely computes the fractional total chromatic number of G n,p for all values of p. ABR ÉG ÉUne coloration totale d'un graphe est le coloration des arêtes et des sommets telle que deux sommets adjacents ont des couleurs différentes, deux arêtes incidentes ont des couleurs différentes, et une arête a une couleur différente de celles des ses extrémités.Si nous formulons le problème de trouver le nombre chromatique total comme un programme linéaire entier, nous pouvons considérer la relaxation connue comme la coloration totale fractionnaire.Dans cette thèse nous présentons un algorithme pour calculer le nombre chromatique total d'un graphe en temps polynomial en moyenne.Nous présentons aussi un algorithme qui calcule asymptotiquement presque sûrement le nombre chromatique total de G n,p pour toute valeur de p.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".