Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
TwinDominationinDigraphsGaryChartrand,estern Whigan Micy ersit Univeter Pelmann, Danky ersit UnivofNatal,Durbanhelle Micultz, h Scy ersit Univofada, NevLasegas VHendaC.art, Swy ersit UnivofNatal,DurbanAbstractAertex vvinadigraphDout-dominatesitselfasell wallertices vuh sucthat(v,)isanarcofD;whilein-dominatesb othitselfandallertices vwh sucthat(,v)isanarcofD.AsetSawin tdominatingsetofDifery evertex visout-dominatedy bsomeofSandin-dominatedy bsomeertex v.Theum minimy cardinalitawin tdominatingsetisthedominationb umer n(D)of.Itwn shothat(D)2p=3forery evdigraphoforderpving hanoertex vofin-degree0orout-degree0.er, v Moreoe we givaNordhaus-Gaddumyp teb oundfor,ande transitivdigraphse we givasharpupp erb oundforthewin tdominationb umer nintermsoforderandum minimdegree.or FagraphG,theupp ertable orienwin tdominationb umer nD O M()istheum maximwin tdominationb umer n(D)er v oalltations orienofG;whiletheer w lotable orienwin tdominationb umer ndom()istheum minimh sucwin tdominationb umer. nItwn shothatforh eacgraphGandteger incwithdom()D O M),thereexistsantation orienDofGh sucthat()=c.1tro InductionDominationingraphshasb eenstudiedely extensivt recenears. yTheb o oky bynes, HaHedetniemi,andSlater[7]istirely enoted devtothisarea.Dominationind cte e dirgraphs,er, ev w hohasnotattractedthesamet amounoftion atteny bhers researc(seetheey surv[6]),exceptforstudyofernels kdigraphs.Anaturaldirectedanaloguetothedominationb umer nofanundirectedgraphistheout-dominationb umer nofadigraphD,de nedasum minimy cardinalitofasubsetStheertex vsetDh sucthath eaciseitherinoranb out-neighourofsomeertex vinS.Theout-dominationb umer nandthein-dominationb umer, nh whicisde ned, analogouslyarestudiede.g.in[5].Inthispap ere wprop oseathird,equallynaturaldirectedanaloguetodominationingraphs.Thetwindominationer numbofadigraphDistheum minimy cardinalitofasubsetStheertex vsetDh sucthath eaciseitherinorb oth,anb out-neighourofsomeertex vinSandb in-neighour(p ossiblydistinct)ertex vinS.or Fterminologyandnotationp ertainingtodigraphs,e wreferto[2].1
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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